Your first entry form will offer you 90+30 or 15+10 and it will not explain either. Here is the whole code, and it takes about a minute to learn.
Reading the numbers
The first number is the base time in minutes, the second is the increment in seconds that gets added to your clock after each move you complete. So 5+3 means five minutes each, plus three seconds a move. A control written 3+0 has no increment at all, and when your five minutes are gone they are gone.
Longer events often use two periods. The standard for serious FIDE events is ninety minutes for your first forty moves, then thirty more minutes for the rest of the game, with thirty seconds added from move one. Reach move forty and the extra half hour appears on the clock by itself; the increment has been arriving all along.
Where FIDE draws its lines
FIDE does the arithmetic before it classifies you: base time plus sixty times the increment, on the assumption that a game runs about sixty moves.
Ten minutes or less is blitz. So 5+0 is blitz, and so is 3+2, which comes to three minutes plus two more.
More than ten and under sixty is rapid. So 15+10 counts as twenty-five minutes and lands in the middle of the rapid band.
Sixty minutes or more is classical, the band that carries standard FIDE ratings. Under this rule 90+30 counts as two hours per player.
Bullet is not a FIDE category at all. It is an online word for one and two minute games, and no official body rates it.
What the sites mean by the same words
Some sites estimate how long a game will really last, taking the base time plus around forty increments, and sort on that: under three minutes is bullet, under eight is blitz, under twenty-five is rapid, and anything longer is classical. That is why 2+1 can land in a bullet pool while 3+0 counts as blitz.
Others are blunter and read the base time only. Under three minutes bullet, three up to ten blitz, ten and above rapid, with correspondence games given their own name again.
So the same 10+0 game is blitz to an arbiter and rapid to a website. Nobody is lying; they are different rulers, and your four ratings measure four different things.
What I would actually enter
If you are trying to get better, play 15+10 or 10+5, and play fewer games than you want to. One game where you thought properly about move eighteen is worth an evening of 3+0, because the thing you are trying to build is the habit of looking at your opponent’s reply, and at three minutes there is no time to look.
Keep the fast stuff for reinforcing what you already know, and do the actual learning on puzzles instead, where you can take as long as you need on a single position. Then check how long a game really takes before you enter a weekend event and discover that a round is four hours.