The PC has graphics cards and video modes, the Amiga has chipsets. These chipsets determine the screen resolutions and color depths that are possible on that Amiga.
The original chipset (OCS) from 1985, found in the Amiga 500 and 1000, consisted of Paula, Agnus, and Denise. In 1989, it was upgraded to the ECS or enhanced chipset by upgrading Denise and Agnus, who now became known as fat Agnus, which I think somehow rude.
1992 the AGA (Advanced Graphics Adapter) chipset was introduced. It was originally named AA (Advanced Amiga) but renamed in Europe to avoid confusion with the UK Automobile Association. How you could confuse these two things, I don't really know, but another, unpublished reason for the renaming may have been that in Germanand the Amiga was always very popular in GermanyAA is a well known nursery euphemism forwell, something you really don't want a chipset associated with.
In the AGA, Agnus was replaced by Alice and Denise by Liza. Games could now run in 256 colors or even high color. The AGA was first introduced in the high-end Amiga 4000, later in the same year there was the Amiga 1200, an entry-level model. As far as I know, existing ECS Amigas could not be upgraded to AGA, but I might be wrong.
For obvious reasons, game developers were a bit reluctant to support the new chipset. If the game did not support ECS, it could not be sold to the majority of Amiga gamers. Therefore most games at least supported both chipsets, at least for a while.