Question about chess ratings

Is the rating formula different for live chess than in turn based chess? I ask this because a 1500 rated player seems much better in live chess than in turn based chess. Also, I've gotten my rating to 2000+ in turn based chess compared to only 1500+ in live chess. I know you get as much time as you like in turn based chess and there is the analysis board and stuff but, still, there seems to be a difference.

Live chess is in some ways harder, because of all the advantages turn-based chess gives you (e.g. analysis boards, time as you mentioned, use of opening databases and so on) which are not permitted in live chess. Most people I suspect, however, do not use these, meaning if you devote a little time to the game, you will probably do much better. It's the old skill v commitment issue.

Yeah, I do tend to be a lot more careful and spend more time on each move in turn-based than in live chess.

The rating formula is the same, but is dependent on the pool of players. The same player with the same formula playing in two different groups of players would expect to have different ratings.