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.
I’ve had good luck with the streaming in Steam. It used to be called in home streaming, but they changed the name and I forget what is called. It works very well in the house, I’ve used it to play some games with difficult platforming and it was fine. It even works over the Internet, although I assume there would be some lag that way. I’ve only played civilization 6 from a different location so I couldn’t tell if it was lagging.
Easy to set up too, just turn on the option for the host and open steam. From the client, log in with the same username and turn it on. When you look at your games, you have the option of playing local or remote.
Make sure you use hardware video decoding, I had a ton of lag before I got that working right
They will be soon