diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 1b0f2f18efb..6dfd824147f 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -26,6 +26,10 @@ New Features
 - Allow negative frequency strings (e.g. ``"-1YE"``). These strings are for example used
   in :py:func:`date_range`,  and :py:func:`cftime_range` (:pull:`8651`).
   By `Mathias Hauser <https://github.com/mathause>`_.
+- Added a ``join="exact"`` mode for ``Aligner.align`` and related classes.
+  (:issue:`7132`, :issue:`8230`).
+  By `Etienne Schalk <https://github.com/etienneschalk>`_.
+
 - Add :py:meth:`NamedArray.expand_dims`, :py:meth:`NamedArray.permute_dims` and :py:meth:`NamedArray.broadcast_to`
   (:pull:`8380`) By `Anderson Banihirwe <https://github.com/andersy005>`_.
 
diff --git a/xarray/backends/api.py b/xarray/backends/api.py
index 670a0ec6d68..80c38a24c44 100644
--- a/xarray/backends/api.py
+++ b/xarray/backends/api.py
@@ -791,13 +791,15 @@ def open_dataarray(
 def open_mfdataset(
     paths: str | NestedSequence[str | os.PathLike],
     chunks: T_Chunks | None = None,
-    concat_dim: str
-    | DataArray
-    | Index
-    | Sequence[str]
-    | Sequence[DataArray]
-    | Sequence[Index]
-    | None = None,
+    concat_dim: (
+        str
+        | DataArray
+        | Index
+        | Sequence[str]
+        | Sequence[DataArray]
+        | Sequence[Index]
+        | None
+    ) = None,
     compat: CompatOptions = "no_conflicts",
     preprocess: Callable[[Dataset], Dataset] | None = None,
     engine: T_Engine | None = None,
@@ -912,7 +914,8 @@ def open_mfdataset(
           aligned are not equal
         - "override": if indexes are of same size, rewrite indexes to be
           those of the first object with that dimension. Indexes for the same
-          dimension must have the same size in all objects.
+        - "strict": similar to "exact", but less permissive.
+          The alignment fails if dimensions' names differ.
     attrs_file : str or path-like, optional
         Path of the file used to read global attributes from.
         By default global attributes are read from the first file provided,
diff --git a/xarray/core/alignment.py b/xarray/core/alignment.py
index 28857c2d26e..b466f8938fb 100644
--- a/xarray/core/alignment.py
+++ b/xarray/core/alignment.py
@@ -5,7 +5,17 @@
 from collections import defaultdict
 from collections.abc import Hashable, Iterable, Mapping
 from contextlib import suppress
-from typing import TYPE_CHECKING, Any, Callable, Final, Generic, TypeVar, cast, overload
+from typing import (
+    TYPE_CHECKING,
+    Any,
+    Callable,
+    Final,
+    Generic,
+    TypeVar,
+    cast,
+    get_args,
+    overload,
+)
 
 import numpy as np
 import pandas as pd
@@ -19,7 +29,7 @@
     indexes_all_equal,
     safe_cast_to_index,
 )
-from xarray.core.types import T_Alignable
+from xarray.core.types import JoinOptions, T_Alignable
 from xarray.core.utils import is_dict_like, is_full_slice
 from xarray.core.variable import Variable, as_compatible_data, calculate_dimensions
 
@@ -28,7 +38,6 @@
     from xarray.core.dataset import Dataset
     from xarray.core.types import (
         Alignable,
-        JoinOptions,
         T_DataArray,
         T_Dataset,
         T_DuckArray,
@@ -145,7 +154,7 @@ def __init__(
         self.objects = tuple(objects)
         self.objects_matching_indexes = ()
 
-        if join not in ["inner", "outer", "override", "exact", "left", "right"]:
+        if join not in get_args(JoinOptions):
             raise ValueError(f"invalid value for join: {join}")
         self.join = join
 
@@ -264,13 +273,13 @@ def find_matching_indexes(self) -> None:
         self.all_indexes = all_indexes
         self.all_index_vars = all_index_vars
 
-        if self.join == "override":
+        if self.join in ("override", "strict"):
             for dim_sizes in all_indexes_dim_sizes.values():
                 for dim, sizes in dim_sizes.items():
                     if len(sizes) > 1:
                         raise ValueError(
-                            "cannot align objects with join='override' with matching indexes "
-                            f"along dimension {dim!r} that don't have the same size"
+                            f"cannot align objects with join={self.join!r} with matching indexes "
+                            f"along dimension {dim!r} that don't have the same size ({sizes!r})"
                         )
 
     def find_matching_unindexed_dims(self) -> None:
@@ -472,12 +481,27 @@ def assert_unindexed_dim_sizes_equal(self) -> None:
                 )
             else:
                 add_err_msg = ""
+            # Same for indexed dims?
             if len(sizes) > 1:
                 raise ValueError(
                     f"cannot reindex or align along dimension {dim!r} "
                     f"because of conflicting dimension sizes: {sizes!r}" + add_err_msg
                 )
 
+    def assert_equal_dimension_names(self) -> None:
+        # Strict mode only allows objects having the exact same dimensions' names.
+        if not self.join == "strict":
+            return
+
+        unique_dims = set(tuple(o.sizes) for o in self.objects)
+        all_objects_have_same_dims = len(unique_dims) == 1
+        if not all_objects_have_same_dims:
+            raise ValueError(
+                f"cannot align objects with join='strict' "
+                f"because given objects do not share the same dimension names ({[tuple(o.sizes) for o in self.objects]!r}); "
+                f"try using join='exact' if you only care about equal indexes"
+            )
+
     def override_indexes(self) -> None:
         objects = list(self.objects)
 
@@ -568,6 +592,7 @@ def align(self) -> None:
             self.results = (obj.copy(deep=self.copy),)
             return
 
+        self.assert_equal_dimension_names()
         self.find_matching_indexes()
         self.find_matching_unindexed_dims()
         self.assert_no_index_conflict()
@@ -576,7 +601,7 @@ def align(self) -> None:
 
         if self.join == "override":
             self.override_indexes()
-        elif self.join == "exact" and not self.copy:
+        elif not self.copy and (self.join in ("exact", "strict")):
             self.results = self.objects
         else:
             self.reindex_all()
@@ -716,6 +741,8 @@ def align(
         - "override": if indexes are of same size, rewrite indexes to be
           those of the first object with that dimension. Indexes for the same
           dimension must have the same size in all objects.
+        - "strict": similar to "exact", but less permissive.
+          The alignment fails if dimensions' names differ.
 
     copy : bool, default: True
         If ``copy=True``, data in the return values is always copied. If
diff --git a/xarray/core/combine.py b/xarray/core/combine.py
index 10f194bf9f5..7f7301db9f8 100644
--- a/xarray/core/combine.py
+++ b/xarray/core/combine.py
@@ -448,6 +448,9 @@ def combine_nested(
         - "override": if indexes are of same size, rewrite indexes to be
           those of the first object with that dimension. Indexes for the same
           dimension must have the same size in all objects.
+        - "strict": similar to "exact", but less permissive.
+          The alignment fails if dimensions' names differ.
+
     combine_attrs : {"drop", "identical", "no_conflicts", "drop_conflicts", \
                      "override"} or callable, default: "drop"
         A callable or a string indicating how to combine attrs of the objects being
@@ -737,6 +740,8 @@ def combine_by_coords(
         - "override": if indexes are of same size, rewrite indexes to be
           those of the first object with that dimension. Indexes for the same
           dimension must have the same size in all objects.
+        - "strict": similar to "exact", but less permissive.
+          The alignment fails if dimensions' names differ.
 
     combine_attrs : {"drop", "identical", "no_conflicts", "drop_conflicts", \
                      "override"} or callable, default: "no_conflicts"
diff --git a/xarray/core/concat.py b/xarray/core/concat.py
index 26cf36b3b07..2dd5b647fdd 100644
--- a/xarray/core/concat.py
+++ b/xarray/core/concat.py
@@ -148,6 +148,9 @@ def concat(
         - "override": if indexes are of same size, rewrite indexes to be
           those of the first object with that dimension. Indexes for the same
           dimension must have the same size in all objects.
+        - "strict": similar to "exact", but less permissive.
+          The alignment fails if dimensions' names differ.
+
     combine_attrs : {"drop", "identical", "no_conflicts", "drop_conflicts", \
                      "override"} or callable, default: "override"
         A callable or a string indicating how to combine attrs of the objects being
diff --git a/xarray/core/merge.py b/xarray/core/merge.py
index a8e54ad1231..aafd60d9ca4 100644
--- a/xarray/core/merge.py
+++ b/xarray/core/merge.py
@@ -790,6 +790,8 @@ def merge(
         - "override": if indexes are of same size, rewrite indexes to be
           those of the first object with that dimension. Indexes for the same
           dimension must have the same size in all objects.
+        - "strict": similar to "exact", but less permissive.
+          The alignment fails if dimensions' names differ.
 
     fill_value : scalar or dict-like, optional
         Value to use for newly missing values. If a dict-like, maps
diff --git a/xarray/core/options.py b/xarray/core/options.py
index d116c350991..453800ea1f7 100644
--- a/xarray/core/options.py
+++ b/xarray/core/options.py
@@ -166,6 +166,8 @@ class set_options:
         - "override": if indexes are of same size, rewrite indexes to be
           those of the first object with that dimension. Indexes for the same
           dimension must have the same size in all objects.
+        - "strict": similar to "exact", but less permissive.
+          The alignment fails if dimensions' names differ.
 
     cmap_divergent : str or matplotlib.colors.Colormap, default: "RdBu_r"
         Colormap to use for divergent data plots. If string, must be
diff --git a/xarray/core/types.py b/xarray/core/types.py
index 8c3164c52fa..44a24dc5501 100644
--- a/xarray/core/types.py
+++ b/xarray/core/types.py
@@ -206,7 +206,7 @@ def copy(
     Literal["drop", "identical", "no_conflicts", "drop_conflicts", "override"],
     Callable[..., Any],
 ]
-JoinOptions = Literal["outer", "inner", "left", "right", "exact", "override"]
+JoinOptions = Literal["outer", "inner", "left", "right", "exact", "override", "strict"]
 
 Interp1dOptions = Literal[
     "linear", "nearest", "zero", "slinear", "quadratic", "cubic", "polynomial"
diff --git a/xarray/tests/test_concat.py b/xarray/tests/test_concat.py
index 0cf4cc03a09..0519a91516e 100644
--- a/xarray/tests/test_concat.py
+++ b/xarray/tests/test_concat.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+import re
 from copy import deepcopy
 from typing import TYPE_CHECKING, Any, Callable
 
@@ -1261,3 +1262,103 @@ def test_concat_index_not_same_dim() -> None:
         match=r"Cannot concatenate along dimension 'x' indexes with dimensions.*",
     ):
         concat([ds1, ds2], dim="x")
+
+
+def test_concat_join_coordinate_variables_non_asked_dims():
+    ds1 = Dataset(
+        coords={
+            "x_center": ("x_center", [1, 2, 3]),
+            "x_outer": ("x_outer", [0.5, 1.5, 2.5, 3.5]),
+        },
+    )
+
+    ds2 = Dataset(
+        coords={
+            "x_center": ("x_center", [4, 5, 6]),
+            "x_outer": ("x_outer", [4.5, 5.5, 6.5]),
+        },
+    )
+
+    # Using join='outer'
+    expected_wrongly_concatenated_xds = Dataset(
+        coords={
+            "x_center": ("x_center", [1, 2, 3, 4, 5, 6]),
+            "x_outer": ("x_outer", [0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5]),
+        },
+    )
+    # Not using strict mode will allow the concatenation to surprisingly happen
+    # even if `x_outer` sizes do not match
+    actual_xds = concat(
+        [ds1, ds2],
+        dim="x_center",
+        data_vars="different",
+        coords="different",
+        join="outer",
+    )
+    assert all(actual_xds == expected_wrongly_concatenated_xds)
+
+    # Using join='strict'
+    # A check similar to the one made on non-indexed dimensions regarding their sizes.
+    with pytest.raises(
+        ValueError,
+        match=re.escape(
+            r"cannot align objects with join='strict' with matching indexes "
+            r"along dimension 'x_outer' that don't have the same size ({3, 4})"
+        ),
+    ):
+        concat(
+            [ds1, ds2],
+            dim="x_center",
+            data_vars="different",
+            coords="different",
+            join="strict",
+        )
+
+
+def test_concat_join_non_coordinate_variables():
+    ds1 = Dataset(
+        data_vars={
+            "a": ("x_center", [1, 2, 3]),
+            "b": ("x_outer", [0.5, 1.5, 2.5, 3.5]),
+        },
+    )
+
+    ds2 = Dataset(
+        data_vars={
+            "a": ("x_center", [4, 5, 6]),
+            "b": ("x_outer", [4.5, 5.5, 6.5]),
+        },
+    )
+
+    # Whether join='outer' or join='strict' modes are used,
+    # the concatenation fails because of the behavior disallowing alignment
+    # of non-indexed dimensions (not attached to a coordinate variable).
+    with pytest.raises(
+        ValueError,
+        match=(
+            r"cannot reindex or align along dimension 'x_outer' "
+            r"because of conflicting dimension sizes: {3, 4}"
+        ),
+    ):
+        concat(
+            [ds1, ds2],
+            dim="x_center",
+            data_vars="different",
+            coords="different",
+            join="strict",
+        )
+
+    with pytest.raises(
+        ValueError,
+        match=(
+            r"cannot reindex or align along dimension 'x_outer' "
+            r"because of conflicting dimension sizes: {3, 4}"
+        ),
+    ):
+        concat(
+            [ds1, ds2],
+            dim="x_center",
+            data_vars="different",
+            coords="different",
+            join="outer",
+        )
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index ab1fc316f77..f8dce0a94ed 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -3188,6 +3188,26 @@ def test_align_str_dtype(self) -> None:
         assert_identical(expected_b, actual_b)
         assert expected_b.x.dtype == actual_b.x.dtype
 
+    def test_align_exact_vs_strict(self) -> None:
+        xda_1 = xr.DataArray([1], dims="x1")
+        xda_2 = xr.DataArray([1], dims="x2")
+
+        # join='exact' passes
+        aligned_1, aligned_2 = xr.align(xda_1, xda_2, join="exact")
+        assert aligned_1 == xda_1
+        assert aligned_2 == xda_2
+
+        # join='strict' fails because of non-matching dimensions' names
+        with pytest.raises(
+            ValueError,
+            match=(
+                r"cannot align objects with join='strict' "
+                r"because given objects do not share the same dimension names "
+                r"([('x1',), ('x2',)])"
+            ),
+        ):
+            xr.align(xda_1, xda_2, join="strict")
+
     def test_broadcast_arrays(self) -> None:
         x = DataArray([1, 2], coords=[("a", [-1, -2])], name="x")
         y = DataArray([1, 2], coords=[("b", [3, 4])], name="y")