On Chess.com, I recently passed 2000 in the puzzle section. However, in 10 minute games, I can't reach 1600. How do I bridge that gap and increase my game score? Is 10 minutes maybe too short of a game to find/apply tactics? I have some theory/strategy knowledge that usually gives me an edge (or at least an equal game) after the opening moves.
On chess.com, my puzzle rating is 700 points higher than my game rating, but my chesstempo puzzle rating is only about 100 points higher than my chess.com game rating. In other words, puzzle rating on chess.com is not comparable with your game rating.
I'd suggest just keep doing 10 (or more) puzzles a day and ignore whatever the gap.
Is 10 mins maybe too short of a game to find/apply tactics?
Absolutely not. Tactics can be found and applied in all time controls. Its more about your ability to locate them and execute it.
How do I bridge that gap and increase my game score?
Puzzle ratings aren't necessarily a good representation of "skill". It is common for individuals to have higher puzzle ratings than their game ratings (Blitz , Rapid more commonly). This makes sense when you think about it as with a puzzle you are analysing a position more objectively. In game you are unlikely to be spending the same duration of time analysing the position and objectively making the correct move.
Ultimately the best way to boost your game rating is to complete lessons, study and play. Think how long you review puzzle positions (5 seconds?) , double that time for each move when you are playing a game.
The first thing to know is that players in your rating range do make tactical mistakes, so you do get chances to show your tactical ability.
Look at your games and be honest, how many mistakes do you miss? This is the most probable reason, as nobody notifies you that your position is winning, so you are not looking as hard for a winning move. There is a great video about cues for when a tactical motif is present in the position: "How is your Tactical Awareness?" by ChessNetwork
Apart from that, chess sadly is not only tactics.
Formulating middlegame plans and technical conversion are two other areas where work put in will result in huge increase of play quality. Learning middlegame plans is best done by studying games in the openings you play and seeing what good players do once fully developed. Learning conversion is a matter of learning endgames mostly.
It seems that about 400 point gap is normal, it is for me on Lichess
However, being disciplined about what moves you consider can improve your rating. Do you consider all checks and captures on every move? What about all checks and captures your opponent can play against your main candidate move before playing it? Even simple checks like this can prevent a lot of blunders. Just take a look at your blunders and see if these checks would've prevented them.
It might be hard to do a check like this in severe time trouble, so 10+10 is probably better.
You're comparing apples and orange. When you do a puzzle, you can take as long as you like (unless it's timed) to solve it. And knowing that there is a solution is in itself an advantage, as opposed to a game situation when you don't know ahead of time that there's a winning move. And I don't think a 10" game gives you enough time to analyze all the possibilities in depth. Noted players who were skilled at quick chess became skilled before they began playing quick games. Botvinnik wouldn't even play quick games. I frankly think you should play slower games first until you become more skilled before graduating to the quicker ones. I know they're more time consuming and may not be as much fun, but you have to decide which is more important to you.