I'm not too familiar with CMaNGOS, but my understanding is that the original MaNGOS is the ancestor of AzerothCore (as well as most other C++ WoW emulators).
The primary differences that come to mind between CMaNGOS and AC are AC's larger and more active community, AC's module system, and CMaNGOS has a relatively good bot (as in, non-human players) system [0].
As an aside, AC does have a playerbots module [1], but my understanding is that it doesn't have the same polish as CMaNGOS's. It's also distributed as a patch to the upstream AC repo instead of a standard AC module, so that can be a pain for some as well.
The primary differences that come to mind between CMaNGOS and AC are AC's larger and more active community, AC's module system, and CMaNGOS has a relatively good bot (as in, non-human players) system [0].
As an aside, AC does have a playerbots module [1], but my understanding is that it doesn't have the same polish as CMaNGOS's. It's also distributed as a patch to the upstream AC repo instead of a standard AC module, so that can be a pain for some as well.
[0] - https://github.com/celguar/mangosbot-bots [1] - https://github.com/liyunfan1223/mod-playerbots