The terminology is unfortunately confusing, as "generator" is so commonly used to refer to either the function or the returned iterator that it's hard to say one usage is more correct. The documentation of the yield statement says
The yield statement is only used when defining a generator function, and is only used in the body of the generator function. Using a yield statement in a function definition is sufficient to cause that definition to create a generator function instead of a normal function.
When a generator function is called, it returns an iterator known as a generator iterator, or more commonly, a generator.
The original PEP introducing the concept says
Note that when the intent is clear from context, the unqualified name "generator" may be used to refer either to a generator-function or a generator-iterator.
If you want to make a clear distinction, use "generator function" for the function and "generator iterator" for the iterator.