After some discussion about call_count vs await_count, I believe call_count should be counting when things are *awaited* (await foo()), not when they are *called* (foo()). 

I think people expect "calling" to execute the code and give them a return_value, which for asyncio is what happens when you await, not when you call with (). If people disagree about this I am open to discussion, we can change the current functionality and leave in the assert_awaited_* calls.

Currently the code does count asyncio calls when they are awaited, but this makes the assert_awaited_* calls redundant. 

We should remove these in favor of the call_count_* functions.

IMO it gives a good segregation between other mocks and AsyncMock that using assert_awaited_* makes it explicit and to cause less confusion over whether this is an awaitable or a synchronous mock. I would favor in keeping the API. I also found it to better in conceptualizing while writing tests for other PRs over having assert_call_* and assert_await_*.

I'm particularly concerned that we have call_count "sane" for AsyncMock and avoid adding "await_count" if possible. I think we've decided on that.

I'm more agnostic on the assert_await* methods. I agree they're a nice API. I don't mind those staying but I also don't mind them going.

Going to try to recap an in-person conversation:

There are some cases where calls are made separate from when they are awaited, for example:
   >>> call = foo()
   >>> await call

This would be 1 call and 1 await:

Call List   Await List
---------   ----------
[foo]        [call]

Calls like:
   >>> await foo()

Should also be counted as 1 call and 1 await, there is no difference between this call and the call above (expect for slight differences in when the lists are updated):

Call List   Await List
---------   ----------
[foo]        [call] 


If someone were to do this:

  >>>call_1 = foo()
  >>>call_2 = foo()

  >>> await call_1
  >>> await foo(x)

We should see 2 calls added to the call list, then 1 await added to the await list, then 1 call added to the call list and 1 await added to the await list. We would end up with 3 calls and 2 awaits. 

Call List              Await List
---------             ----------
[foo, foo, foo]        [call_1, foo]


And a call without an await:
 
  >>> call = foo()

Call List              Await List
---------             ----------
[foo]                 []



With a setup like this, we would keep the API the same (leaving in the assert_await*). There is some risk that users will incorrectly be using assert_call* when they really want to test awaits, but we can try to make to docs as clear as possible around this.

New changeset ef048517755db1f0d211fb6dfc655a8b412cc96f by Lisa Roach in branch 'master':
bpo-38136: Updates await_count and call_count to be different things (GH-16192)
https://github.com/python/cpython/commit/ef048517755db1f0d211fb6dfc655a8b412cc96f

New changeset 52bdd414ed9da7c62c312c542803753986a0040a by Lisa Roach in branch '3.8':
[3.8] bpo-38136: Updates await_count and call_count to be different things (GH-16192) (GH-16431)
https://github.com/python/cpython/commit/52bdd414ed9da7c62c312c542803753986a0040a