How are people so good at puzzle battle?

People my rating in puzzle battle (1300-1400) seem to be much worse at regular chess like they also have a 1400 blitz/rapid raring while I have a 2k rating in both. 

I don't understand how this is possible, am I especially bad at puzzle battle? Is everyone cheating? Is there no correlation with chess skills? Wtf?

No answers? I'm leaning on the I'm especially bad at puzzle battles, it's sometimes hard for me when the board just change position from white to black, it can take me up to a few seconds to just recognize what am I looking at. Even before calculating anything.

The reason why some people are incredibly good at puzzles but mid in actual chess is because puzzles always have a solution, in real chess that’s not always the case. Another reason might be pattern recognition. Do puzzles long enough and you might comes across patterns you’ve already seen before making it easier to do. Me personally I see chess puzzles and chess as 2 distinct things, practicing puzzles doesn’t make you good at actual games and playing actual games doesn’t make you good at puzzles. My advice to you is 1. Don’t do puzzle battles anymore. If they’re causing you to feel like you’re mid at the game then stop. 2. Continue doing puzzles. Puzzle solving skill is all about repetition, it takes times but in a few weeks you’ll see drastic improvement assuming you’re practicing on a day to day basis.

I hope this helps .

Having watched the Top Battle for awhile I am equally confused; the first 20 puzzles seem to be solved within 0.1 seconds. It appears AND vanishes before I can blink.

Now I understand being able to quickly see the best move (I'm 2224 puzzles), but the exact move is ALSO made at insane speed... How do they get the mouse at the exact position to grab the piece THAT fast, it seems impossible?

Also, after the first blitzing spree the actual puzzle solving seems to go a bit TOO slow, for such amazing ability.
EDIT: Some equally super highly rated players seem to NOT blitz the start at that insane speed, and then win later on by being consistently fast and accurate.