any brand of bits will g fit any brand of drill/driver. The hexagonal bodies are standardized.

But when I referenced the two brand names I was referring to manual hand held drivers

For example, in the amazon page ( infra) there are any number of driver bits made by wiha, and you san see that there are manual handles plus they will fit any hex drive impact drill/driver doesn't matter if it's Dewalt, Riobi, or Milwaukee they are all the same.

https://www.amazon.com/wiha-driver-bits/s?k=wiha+driver+bits