Its a very different experience playing chess online from your couch or a bench etc. and playing against real people face to face. The noise, the lights, the pressure of playing for something that's "real" as the person above mentions. Some people find it easier other harder but no the rating will never really be the same.
Accuracy of rating in Chess.com versus tournament play


For some there may be some correlation, for others, not so much.

I have only played daily and I would think for daily games the ratings here would be higher, since you have several days to play over a position and decide on a move. You can go away from the game, relax, "sleep on it", come back refreshed and perhaps see something you might otherwise have missed.
As noted above, playing OTB with the attendant distractions and time constraint is added stress that could very well detract from your game. Whereas in the comfort of your home with several days to make decisions, now you need to move now, now, now.
On the other hand, both players have that same advantage of relaxation and time. I have played games where my opponent made really good moves and the occasional questionable move. But they took little time making their moves, sometimes only minutes. I felt after a few of those games I was lucky to win because had they taken the time, they would likely have made different moves and won those games. This would mean my rating would be lower (but theirs higher). So, after writing all of this, now I'm not so sure!!
I don't think so. Most people only put in half their concentration when they are playing an online game game that wont count towards anything, so the ratings online are jumbled. It seems like most people are over rated in bullet, many of my USCF 2000 friends have 2400+ bullet ratings. Quick ratings also seem to be inflated. Personally my ratings on here are much lower than my USCF, so i guess it just depends on the person. I don't think the ratings on this website will ever be accurate because people play differently when it isn't counting towards any federation.