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.
While the ECS allowed higher resolutions, this did not have any impact on games, which used the same 320×256 (or 320×200 on NTSC), 32-color mode under both chipsets.
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. It allowed games to run at 640×480, but was supported somewhat reluctantly by game developers.