Puzzle battle: same puzzle for both players?

Hi, i'm somewhat a newcomer, i've recently taken a liking to the puzzle battle as an alternative to the regular games. It came to my attention that alot of time, it's either me quickly completing a bunch of puzzles in a row or my opponent. I was wondering if the puzzle were the same for both players? Sometimes it just feels impossible to take such a lead or for my opponent to take such a league (i'm 650ish rating for puzzles battle). 

Yes, they are the same for both players.

I got a puzzle the same position as one of my games

I dont think the puzzles are same for both players. Actually I believe that players with paid subscriptions have an advantage like getting a bit easier puzzles. I consider myself as a person with quite good tactical vision, but still on puzzle battle Im very often beaten by people rated 1500 - 1600 which are doing like 30 + correct puzzles for less than 2 minutes, which is ridicilous taken into account their rating and compared with my blitz/rapid rating. So conclusion is quite simple for me - either something wrong with chess com rating system, either something sucks on puzzle battle