Again, there is no APU specific driver. Download the drivers for your chipset and graphics device matching what is built into your "APU", and you should have what you need. Also, AMD no longer refers to the Ryzen based CPUs with integrated graphics as APUs, not that it makes much difference other than for clarity.

Do I need to install APU drivers?

You shouldn't have any need to install both drivers. The APU drivers are already there. If you choose, you can probably install both of them without any issue as they are totally separate entities. However, there's really not a reason to.

What is the AMD APU driver for?

It's a universal driver for all gpus and apus. If you install it, it will detect and update all amd-related hardware drivers accordingly.