diff --git a/discord/client.py b/discord/client.py
index fae80832b9..8c85ea8441 100644
--- a/discord/client.py
+++ b/discord/client.py
@@ -213,9 +213,9 @@ class Client:
         Defaults to `1` second.
 
         .. versionadded:: 2.5
-    maximum_rate_limit_time: :class:`int`
-        The maximum amount of seconds the client is allowed to wait on a rate limit,
-        or otherwise error out. Defaults to `-1`, or infinite.
+    rate_limit_timeout: :class:`float`
+        The maximum amount of seconds the client is allowed to wait on a rate limit
+        before raising an exception. Defaults to `-1`, or infinite.
 
         .. versionadded:: 2.5
 
@@ -251,6 +251,7 @@ def __init__(
         bucket_storage = options.pop("bucket_storage_cls", BucketStorage)(
             options.pop("per", 1), options.pop("concurrency", 50)
         )
+        rate_limit_timeout: float = options.pop("rate_limit_timeout", -1)
 
         self.http: HTTPClient = HTTPClient(
             bucket_storage,
@@ -259,7 +260,7 @@ def __init__(
             proxy_auth=proxy_auth,
             unsync_clock=unsync_clock,
             loop=self.loop,
-            maximum_rate_limit_time=options.pop("maximum_rate_limit_time", -1),
+            rate_limit_timeout=rate_limit_timeout,
         )
 
         self._handlers: dict[str, Callable] = {"ready": self._handle_ready}
diff --git a/discord/http.py b/discord/http.py
index 2ef827523f..c2f53a53df 100644
--- a/discord/http.py
+++ b/discord/http.py
@@ -144,7 +144,7 @@ def __init__(
         proxy_auth: aiohttp.BasicAuth | None = None,
         loop: asyncio.AbstractEventLoop | None = None,
         unsync_clock: bool = True,
-        maximum_rate_limit_time: int | float = -1,
+        rate_limit_timeout: float = -1,
     ) -> None:
         self.loop: asyncio.AbstractEventLoop = (
             asyncio.get_event_loop() if loop is None else loop
@@ -156,7 +156,7 @@ def __init__(
         self.proxy: str | None = proxy
         self.proxy_auth: aiohttp.BasicAuth | None = proxy_auth
         self.use_clock: bool = not unsync_clock
-        self.maximum_rate_limit_time = maximum_rate_limit_time
+        self.rate_limit_timeout = rate_limit_timeout
 
         user_agent = (
             "DiscordBot (https://pycord.dev, {0}) Python/{1[0]}.{1[1]} aiohttp/{2}"
@@ -313,12 +313,12 @@ async def request(
                                 is_global: bool = data.get("global", False)
 
                                 if (
-                                    retry_after > self.maximum_rate_limit_time
-                                    and self.maximum_rate_limit_time != -1
+                                    retry_after > self.rate_limit_timeout
+                                    and self.rate_limit_timeout != -1
                                 ):
                                     raise HTTPException(
                                         response,
-                                        f"Retrying rate limit would take longer than the maximum of {self.maximum_rate_limit_wait_time} seconds given",
+                                        f"Retrying rate limit would take longer than the maximum of {self.rate_limit_timeout} seconds given",
                                     )
 
                                 if is_global:
@@ -346,7 +346,7 @@ async def request(
                                 continue
 
                             # we've received a 500, 502, or 504, unconditional retry
-                            if response.status in {500, 502, 504}:
+                            if response.status in (500, 502, 504):
                                 await asyncio.sleep(1 + tries * 2)
                                 continue