Between 1500 and 1800 it's mainly "tactical play" (which includes seeing threats, recognizing tactical opportunities, calculation...), but also familiarity with your openings.
There may be also some psychological factors involved sometimes (ie. risk aversion / lack of confidence).
However, to answer this question for yourself, you can simply analyze games you lose against stronger players and try to determine the causes of these losses.
For your second question, about 1800-2100 and higher, I refer you to this post: http://www.chess.com/article/view/deep-thinking-and-the-differences-between-titled-players
For your first (I'm speaking as a 1600+ OTB player), anyone under about 1400 USCF usually gives me a piece at some point in the game via a simple blunder, missing a 2-move threat, something like that. Oh, I can take your knight on f6 with my e4 knight, giving check, and then take your unprotected b7 bishop with my g2 bishop--that sort of thing.
Class C (1400-1600), tend to still make calculational errors (I once planned out a 7 move combination to win a piece, only to notice halfway through that my opponent had a knight protecting the piece I planned to win, and it had just been sitting there. I simply didn't see it.) I've also noticed their endgame technique isn't that great--they'll win simple ones, but they don't have a lot of technical skills; think king and pawn triangulation, things like that. I think sometimes they also don't see some basic positional things that need to be accounted for, and that puts them in bad positions where tactics don't favor them.
Class B also misses some positional things, but usually has a plan that makes some sort of sense. They can calculate endgames much better. I haven't played all that many, so I should probably stop here.
If your rating on ICC or FICS is close to your OTB rating, I'd say you beat people because you put some pieces on better squares, have a more focused and coordinated attack, or they blunder some material. Someone 200-300 points higher than you will beat you because they'll have seen a tactic a few moves sooner than you, and that lets them play a move you discounted as impossible, or they'll tangle you up in your own pieces positionally, so you can't execute any sort of plan, while they still can, or they'll simply out-calculate or out-technique you in an endgame. Be particularly careful about middlegame to endgame transitions, as the more endgames they know, the more intelligently they can direct the trades and structural changes to benefit them in the resulting endgame.
Interesting because that's my experience between class C and B too. That Bs usually follow some kind of plan while Cs may have a plan for a move or two but then randomly stop.
But that's really general. Different players have different strengths (opening, middlegame, endgame). The biggest difference is as hicetnunc said, the frequency of tactical blunders. The ability to calculate cleanly is probably the single biggest difference between any two players U2000 (spot tactics, and render a fair evaluation of a future position)
Above that I can't say. Ask a master 
Oh, there is a Karpov quote though. They asked him when he was world champion what distinguishes him between other top grandmasters. He said he plays the opening a little better, sees a little more tactics, knows a little more endgame etc.
There are also some factors you might not think of though, as hicetnunc mentioned about confidence. Time management is one (I'm thinking OTB tournaments here). Not just so you're not running out of time, but how you use the clock to your advantage. I played one player who very effectively avoided complications until I was low on time, then he made a big mess for me. Maybe this is common but I didn't realize what was happening until after it had happened.
Hi,
I have an Elo rating of around 1450 on ICC and around 1590 on FICS (I haven't played here yet - correspondence chess not my thing really). I dont have a FIDE rating.
Anyway, my question is what distinguishes an Elo 1500 player from, lets say, an Elo 1800 player? I know I cannot expect any definitive answer to this question and that there are many determening factors... But I do know how and why I am able to beat a 1200 player easlily most of the time: tactics. I simply "see" a little bit more what's on the board than a 1200 player.
Is that the same reason why an 1800 rated player would beat me (a 1500 player) most of the time? Or do other factors - e.g. positional play - play more of a roll at this level? Or is positional play perhaps the dominant factor between a 1500 and an 1800 rated player?
And what about the difference between an 1800 and a 2100 rated player? And 2100 - 2500; 2500 - 2800.
Does anyone have any thoughts on this?
A.