Honestly, I’m still a beginner anyway, so rank doesn’t mean much, but my life just doesn’t allow me to play in any other way than correspondence. Hence, it’s the only rating that grew, resulting in an overall one that is higher than any of the speed specific ranks.
Some discrepancy can be extremely large. I played with a 25k for correspondence game on a 9 stone handicap, but struggled a lot and then found he/she actually had 15k overall and live ranking. I just quit quickly and felt really wasted my time on that. The system should cap the difference, say no more than 5k difference. 9k to 10k difference is not real.
Indeed, I just requested (and got) my rank manually adjusted by a mod for the same reason – I only played correspondence mostly, and when I started playing live, my live rank was very misleading. (Also, my “correspondence” rank was lagging behind my “overall” rank even though I had only played correspondence, which I found very odd. It really feels like a bug although I think I saw someone claim to explain it once.)