Changing Environment Docstrings
diff --git a/gym/core.py b/gym/core.py
index 797f9216049..8d957ba6e20 100644
--- a/gym/core.py
+++ b/gym/core.py
@@ -65,7 +65,7 @@ def step(self, action: ActType) -> Tuple[ObsType, float, bool, dict]:
             observation (object): agent's observation of the current environment
             reward (float) : amount of reward returned after previous action
             done (bool): whether the episode has ended, in which case further step() calls will return undefined results
-            info (dict): contains auxiliary diagnostic information (helpful for debugging, and sometimes learning)
+            info (dict): contains auxiliary diagnostic information (helpful for debugging, logging, and sometimes learning)
         """
         raise NotImplementedError
 
@@ -76,11 +76,13 @@ def reset(
         """Resets the environment to an initial state and returns an initial
         observation.
 
-        Note that this function should not reset the environment's random
-        number generator(s); random variables in the environment's state should
-        be sampled independently between multiple calls to `reset()`. In other
-        words, each call of `reset()` should yield an environment suitable for
-        a new episode, independent of previous episodes.
+        This method should also reset the environment's random number
+        generator(s) if `seed` is an integer or if the environment has not
+        yet initialized a random number generator. If the environment already
+        has a random number generator and `reset` is called with `seed=None`,
+        the RNG should not be reset.
+        Moreover, `reset` should (in the typical use case) be called with an
+        integer seed right after initialization and then never again.
 
         Returns:
             observation (object): the initial observation.
@@ -94,8 +96,8 @@ def render(self, mode="human"):
         """Renders the environment.
 
         The set of supported modes varies per environment. (And some
-        environments do not support rendering at all.) By convention,
-        if mode is:
+        third-party environments may not support rendering at all.)
+        By convention, if mode is:
 
         - human: render to the current display or terminal and
           return nothing. Usually for human consumption.

I have made some changes to the docstrings of the `Env` methods.
`reset`'s docstring states that 

> this function should not reset the environment's random number generator(s);

If I understand correctly, this used to be true before `seed()` was deprecated. In the current code, it seems that `reset()` is supposed to reset the RNG if

- No RNG exists yet
- The keyward argument `seed` is an integer 

I have changed `reset()`'s docstring accordingly. Is my interpretation of the code correct?


Moreover, @RedTachyon suggested some changes to the Gym documentation in  https://github.com/Farama-Foundation/gym-docs/pull/77 that are also applicable to the docstrings:

- Mention that `info` may contain metrics for logging
- Change "And some environments do not support rendering at all." to "And some third-party environments may not support rendering at all." because all native Gym environments should support rendering in some form.

Formatting of the docstrings seems to be very inconsistent in general, and some docstrings don't list their method's arguments. I have not made any changes in those cases, but this might be an avenue for future improvements.