The steamlink app and the regular steam app are the two clients. I don’t think they work any differently, but steamlink is remote only. I use the regular steam app but have used steamlink too.
Some games don’t work based on how they are made, but steam will let you try with anything. I’ve had some games where controllers don’t work because the game is looking for input on a way that steam isn’t sending.
Funny, but this isn’t the best example. The Atlantic has been a subscription magazine for coming on 200 years now. It’s also one of the few places you can get non click bait articles without ads.