The main difference is in the pace - blitz is when you have very little time (a couple of minutes per game), rapid is longer, and classical is even longer. The rules are the same on both sites, except Lichess is free and more open, while Chess.com offers paid features, though there's still plenty of stuff you can do for free. Rating works the same everywhere: you win and it goes up, you lose and it goes down, depending on your opponent's rating. Just try whichever one has an interface that feels more comfortable to you - there's no real difference in how the game itself plays out.