2.4 GHz Controllers

I know the Retro-Bit 2.4 GHz Genesis/Saturn Controllers will work on either Console

Will the 8-BitDo 2.4 GHz SNES/Genesis Receiver work on the Retro-Bit Genesis/Saturn Controller or does it have a different frequency or channel?

Nope, 2.4 Ghz wireless decides are usually fixed/encoded to their dedicated dongle.
If you want to mix and match, you want to use Bluetooth. And yes I know Bluetooth has lag.