Open Source AMD edit
AMDGPU is the next generation family of open source graphics drivers for newer AMD/ATI Radeon graphics cards based on the Graphics Core Next-chipsets, ranging from GCN1 (Radeon HD 7000) up to the latest graphics cards.
The radeon driver is an open source driver for fairly all ATI Radeon cards.
Proprietary AMD edit
AMDGPU-PRO is the next generation closed source graphics component that operates on top of the open source AMDGPU drivers for newer AMD/ATI Radeon graphics cards.
For Radeon GPUs HD 5xxx or above
Radeon GPUs HD 4xxx or below should use the open-source radeon driver