Skills required for blitz/bullet vs. correspondence chess? I've started playing blitz/bullet (fast) games and felt like I was getting moderately good at it (1 - 10mn games), but then I switched to correspondence chess (1 - 5 days/move) and it seems to me that it was affecting my fast games skills.

Does correspondence chess really require a different set of skills than fast chess? Do you have any advice that may help getting the best of both type of games?
While the two are vastly different, if you improve at one, you will most likely also improve at the other.

Tactics are far more important to get right in correspondence chess.  The slightest misstep will be punished by your opponent simply because they have all the time they need to analyze all of the variations, and they can also use at least a board to assist them, and in some cases, even a chess engine.  

In blitz chess, while attacks frequently win the game, unsound moves are not always refuted.  This means that if you are able to launch an attack, even at the cost of a piece, your opponent will most likely be forced to burn time in order to avoid mate, and this will give you an advantage on the clock.  

In terms of long term planning, in correspondence chess, assuming a high level game where tactical blunders will not determine the result, plans become incredibly important.  A correspondence game is frequently a battle between two plans while in blitz chess, tactics and the clock rule the day.

So overall, correspondence chess is a much higher quality game.  Blitz chess is fun and quick (so you can play a lot more games), but in terms of getting better at chess, blitz won't really help you.  If you want to improve at blitz, practice tactics and play more blitz!