The Apple III was meant to be a business machine. There was software that allowed it to emulate an Apple II but you couldn't run Apple II software without first running that emulation software. So in some ways that made it more like an Apple II emulator on a Mac or PC. A IIgs will directly boot apple II software. Actually an Apple III won't run a lot of Apple II software. It won't run anything that needs more than 48k RAM or 80 column or does a lot of hardware pokes. So a lot of games and some other software wouldn't run on it but almost all would on a IIgs.

When the IIgs was due to come out a lot of people bought 65802s for their Apple II. Almost all were people that wanted to learn to program for the IIgs There's only a couple of Apple II programs that'll utilize a 65802. Sort of a pity but understandable.