Puzzles --> Puzzles. Chess.com has 150k puzzles in various categories. You can go through the puzzles and get a hint if you need it. As you solve puzzles you get a rating. All puzzles have a target time and if you beat it you get more rating. Sometimes if I can't solve a puzzle quickly I grind it until I find the answer and get like 1 point which still beats getting puzzle wrong. There is also a graph of your progress and later you can see your stats and see what categories you need to work on.

Puzzles --> Puzzle Rush. Back when this feature came out this was the reason I got a paid account so I could play it more than once a day. This is basically doing puzzles but with a 3 or 5 minute timer. If the time runs out or if you get three strikes the game ends and you're trying to solve as many puzzles as you can (and there's a leader board). There is also a survival mode with no timer but still three strikes ends the game. It's a pretty addictive mode.

Puzzles --> Puzzle Battle. After the success of Puzzle Rush they came out with Puzzle Battle which is Puzzle Rush vs another player. You're both doing the same puzzles. You have a Puzzle Battle rating which goes up and down as you win and lose games.

Puzzles --> Daily Puzzle. Like a newspaper chess puzzle.

Puzzles --> Solo Chess. Chess pieces are set up on the board. Capture pieces until there is only one left but no piece may capture more than two times and the King (if any) must be the last one standing. I guess the aim is to practice capture combinations. There is no scoring and the challenge mode is either you finish it or not so it kind of lacks gamification.

Puzzles --> Chess Drills. Here you can choose a category and practice puzzles based on a theme.

I do the Puzzles and Puzzle Rush. I just did my first Puzzle Battles today. Overall I probably use this section the most.