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https://docs.python.org/3/reference/expressions.html#yield-expressions
Current:
"""
When a generator function is called, it returns an iterator known as a generator. That generator then controls the execution of a generator function. The execution starts when one of the generator’s methods is called.
"""
At a minimum, that seems to be using "generator function" in two different ways, but I think there are other problems.
Proposed:
"""
When a generator function is called, it returns a special kind of iterator known as a generator. The iteration starts when one of the generator’s methods is called.
"""

You can't just drop the middle sentence. Awkward though it is, it is attempting to describe that the generator object controls suspension and resumption of the stack frame representing execution of the generator function's body.

Yes, and it is not using generator function in two different ways: it is literally the case that calling the generator function returns a generator object, which in turn controls the execution of the generator function. The text then goes on to explain how this works.
I think it would make sense to change "controls execution of a generator function" to "controls execution of the generator function", but I can't think of any other change that would make things clearer.

OK, then how about
Current:
"""
When a generator function is called, it returns an iterator known as a generator. That generator then controls the execution of a generator function. The execution starts when one of the generator’s methods is called.
"""
Proposed:
"""
When a generator function is called, it does not complete its execution immediately. Instead, it keeps its execution frame intact, and returns a special kind of iterator known as a generator. The iteration starts when one of the generator’s methods is called, and the generator executes within the existing generator frame, rather than creating a new one.
"""
This still seems to suggest that the generator uses the same frame as the generator function that created it; I was not aware that this was a guarantee. (Reusing the same frame, yes. Reusing that particular frame, no.)

I don't think anything about frames is guaranteed as part of the language, so I'm not sure that mention of it belongs in the description. Personally, I find your reformulation more confusing that the original with 'a' replaced by 'the'.

New changeset b87d96e0708e by Guido van Rossum in branch '3.4':
Issue 24088: Clarify semantics of yield expression.
https://hg.python.org/cpython/rev/b87d96e0708e 

New changeset 6e59d82d3d09 by Guido van Rossum in branch 'default':
Issue 24088: Clarify semantics of yield expression (merge from 3.4).
https://hg.python.org/cpython/rev/6e59d82d3d09