Yep, you got it pretty nailed down.
Carbon -> carbon , paste.
Alloy -> alloy, grease (maybe anti-seize for pedals, but grease is what I've always used)
I use an alloy seatpost in a carbon frame, and I use paste for that always.
Anything on carbon, paste in my opinion, carbon steerer especially. I don't know if you have to use anything on the steerer FWIW.
That's it pretty much.