Discrepancy in rating between chess sites, a cheating phenomenon?

I enjoy playing here a lot. I have noticed that games are a lot more "natural" here, with even 2100 players blundering a pawn or allowing a mate in one. Even GMs blunder.
It has been a long while since I have played on chess.com, icc, and the chessbase site.
On the other sites, I struggle to beat 1500 players. Apparently, they are excellent endgame players and understand deep positional ideas.
I have been playing on and off for more than 20 years, and at my highest, I was about 2000 OTB.
Lately I have been studying a lot, especially endgames. I KNOW that I am much stronger now, but since I have not played OTB for a while, I cannot validate it.
In the past month playing here, I got up to about 2070. Which sounds pretty realistic. My opponents are strong but they are not perfect, especially in 5 minutes and 10 minute games (I dont play bullet).
In those sites it is very hard to get past 1900 ( in one of those sites my blitz is at 1600!).
I would assume that if my chess strength is the same, the results should be similar.
But they are not.
IMHO there is a LOT of cheating, especially on the paid sites.
There it is common for 1400 players to understand deep opening theory and blitz out the moves.
Here it is a lot more normal, as one would see on OTB situations.
I think I have found the right place to play!

It's all different rating systems, so they really can't be compared.

Rating systems are different, see: lichess.org/faq#ratings and lichess.org/page/rating-systems.

No idea honestly. I just played my old friend who plays almost exclusively on chess.com now and I beat him 3x in a row.

But I do think chess.com is seen as the more "official" chess site in terms of attracting the most verified, over-the-board style players. ex: club players

I do agree play here is very natural, which I actually find kind of funny. I find myself struggling against 1600 - 1800 players in bullet more than I do players my own rating. The amount of blundering tactically at this level is insane, even though strategy is much better.

Too bad there aren't good puzzle games to teach strategy AND tactics. I end up having to take 5x the time to analyze puzzles in order to try and get the best of both worlds.

Even if there's lot of cheating Lichess and chess.com both have great cheat detection system.
And for ratings see the faq as there are different rating systems and everyone doesn't use same method.
For rough comparison,
Lichess rating + 400 = Chess.com rating

Biggest thing about rating that they are relative. Your actual chess skill is not measured only how you win lose against opponents is same pool. Chess.com default starting rating is 1200 and lichess has 1500 this creates a difference on of 300 points alone. Next thing is who is playing in the pool. Though I dont't thing there is much difference. Impact of Gliko-1 vs Glicko-2 is insignificant as the difference only affect how well system track improving/declining players.

so matter where you go you cannot expect same number to mean same playing level

It has nothing to do with cheaters, it has everything to do with the rating system and player pools.

-Jordan

When some websites start you at a rating of 300 less than here, you can't expect to have equal ratings.
You've got some fantastic answers above!

What different chess sites have in common: the same conspiracy theories.