What's the difference between research APC 1 and class APC research?

The APCs are the armies that you can used from the Barracks that you build. There are 3 normal Barracks to build that give you APC 1, APC 2 and APC 3.

There is also a Class Barrack that you can build that gives you the Class APC but it is also known as APC 4 (it was originally APC 4 but was renamed as the Class APC although hasn't been updated everywhere).

The class APC has certain benefits depending on the class you are playing as.