...does this much difference in rating signal that it is possible that one is cheating?
Nope. I'm about 1480 in regular, and an awful 650+ in Random Chess. Rating is an indicator of where you stand in the population, and some people are just really good at certain variants.
I think it is very odd.
Some people have lost quite a few games on disconnections. If they only have a handful of games this could be an answer. The strange thing is, that if you were to cheat at correspodence chess, why only go for 2000?
*also, where has the spell check button gone? Do I have to think now - on my day off too!
Well to cheat in 100% of your games with 100% of your moves is pretty boring unless you're a deranged sociopath 
but a difference of 1000 points... maybe they just use a weaker engine like a handheld thing for a lot of hints as they play.
The spell check button (which I use often because I can't hardly spell) has turned invisible, but it's still there. The gray box shaped gap in the middle between other buttons will spell check for you. It doesn't bring up a box saying all done or no errors anymore, it just does it automatically/instantly.
I don't mean to hi-jack the thread, but, I have no little grey box shaped gap between the other buttons. It's all tight in a little row.
I even spelt a word wrong and then clicked all over my box to see if something would happen....no dice.
Tried to take a screen shot, but this is a work's computer and it refuses to cooperate. I think it's trying to get me to work. The machines are rising!
Also, maybe it is a phone app chess game. I had a friend that used his phone against me once on the sly. I took it apart with my mad skillz 
Whats "normal " on the internet certainly is NOT normal irl !
Why is that the case?
...does this much difference in rating signal that it is possible that one is cheating?
Nope. I'm about 1480 in regular, and an awful 650+ in Random Chess. Rating is an indicator of where you stand in the population, and some people are just really good at certain variants.
Chess960 is different in a lot of ways. I'm not talking about FRC or Chess960. I'm talking about between live and correspondence.
Over 2000 in correspondense and 1000 in live seems a little fishy.
I'm unsure what "standard" time means, as I do not play Live chess.
However, neither correspondence nor internet chess are the true measure of one's chess ability. Live chess usually means quick, piece trading chess (if time is a factor) and correspondence is the exact opposite. For example, pick a GM (any GM) and they can play tournament time with unrivaled strength. Take that same GM and put them in a 15 minute game and they play like an average duffer like you or me. I've seen it live. I've watched 2500+ chessmasters get brutalized by young kids whose specialty are quick games. Impossible to be elite in both arenas.
So, in answer to the question, no red flags should be risen in this instance.
I dont want to accuse you of anything here (lying or exagerating). but, i must be honest: I find it exceptionally hard to believe that a GM would play like a patzer in faster time controls. A GM would be able to rely on his vast library of positional knowledge stored in his head and thus would often be able to find the right move without even thinking.
and also, if i remember correctly. Fischer proved you can master both arena's: http://www.bobby-fischer.net/bobby_fischer_speed_chess.htm
In anycase, to the question at hand. on other relevant bit of data we need is the no. of games played. if it is only a few games than his rating might not be reflective of his skill. but 1000 live for 2000 corr sounds odd.
I have to say I do not agree with this assumption either. GMs are some of the strongest players with fast time controls. If anything, I'd rather play a GM with long time controls than short (blitz) as I would feel my chances to be better, not much, but better.
"Impossible to be elite at both" ~ Masturmater_1
I don't think so. Tell that to the Grandmaster of today like Anand, Carlsen, Topalov, and even the retired Kasparov; see what they have to say about it.
"but 1000 live for 2000 corr sounds odd." ~ Blackadder
I can agree.
*I think I read somewhere that Masturmater_1 was booted, but don't quote me on that.
accusations in forums, trash talking during live chess
is it normal, its rare but it happens
maybe an opportunity was missed to reduce the ratings, when the rds got adjusted a few months back
>:)
It's possible, but I don't think very normal.
My Blitz rating is close to 1000 and my correspondence rating is mid 1700. I lose Blitz all the time to faster player. Often I get a material advantage and lose time, so what would my blitz be without mistakes?
Also, to respond to the comment above, correspondence requires no opening knowledge. You have all sorts of books to read, etc.
I have played quite a few 900 blitz player who just do a good job with the clock.
People get confused and think that rating points are an absolute measurement and not relative to a pool of players. This misunderstanding may be nurtured by the thought that players blunder less the more time they have to think and is reinforced by chess.com's largely disproportionate ratings (CC vs live).
I always laugh when someone says, my CC is ____ hundred points higher than my live because I have more time to think. No, on this site all players have this difference. As the gap approaches 500 it likely means you suck at speed chess and/or lean heavily on the analysis board and databases. As the gap approaches 1000 it likely means there are two players under the same account or you're cheating.
My Blitz rating is close to 1000 and my correspondence rating is mid 1700. I lose Blitz all the time to faster player. Often I get a material advantage and lose time, so what would my blitz be without mistakes?
Slight difference is that this person cannot get a rating of over 1000 in live games versus opponents with an average rating of less than 900. The highest rated opponent this guy has defeated is a dozen points over 1000 and his correspondence rating is over 2000, not 1700.
Also, to respond to the comment above, correspondence requires no opening knowledge. You have all sorts of books to read, etc.
Yes it is true that you do not need to memorize line in correspondence, but you to achieve over a 2000 rating would require basic opening knowledge which should translate into basic opening knowledge in live games.
I have played quite a few 900 blitz player who just do a good job with the clock.
We're not just talking about Blitz here. Even so, "good job with the clock" does not necessarilly mean good or great play.
I dunno, it seems to me that some people just really suck when it comes to having to play under the pressure of time, tick-tock. Perhaps this guy is one of them and he just is good when he has time to really work through things. Also, aren't computer allowed in correspondence chess nowadays? Also, maybe the guy's got a terrible opening and the opening books are getting him through that part of the game...