If you are playing in the app with your iPad , there isnt any option to play match play on a chosen course. You can play one to one with a friend but no choice of course, and no multiplayer options either .
You are certainly correct as to iPad vs. iPad (or phone). However, I could be wrong, but I think a PCEA player can invite a mobile iPad player to a match play game on a specific course. But, they have to be friends first.