On this website at least, of those options in your visual aid: 3|0, 3|2, 5|0, 5|5 and 10|0 are blitz. 1|0 and 2|1 are bullet. 15|10, 30|0 and 45|45 are rapid/standard. If you set a custom game up you can tell by which section of the graphic display your "dot" appears in, but it's generally obvious anyway.
What is blitz?

ok, thanks. btw OT: I dont like watch bullets here even if GM's play them. I can't follow. They are too fast. I would learn if I can first think what I would move. Those games in Live match that can be viewed seems only be 3 mins? Or are here for example 30 mins games to view?

What are the exact definitive thresholds to classify a game as bullet, blitz or rapid based on base time and increment (if any)?

On chess.com, bullet is <3 minutes, blitz is <15 minutes, and standard is everything else. In OTB play, bullet is the same, blitz is from 3-10 minutes, rapid is from 10-60 minutes, and standard is from >30 minutes.

On chess.com, bullet is <3 minutes, blitz is <15 minutes, and standard is everything else. In OTB play, bullet is the same, blitz is from 3-10 minutes, rapid is from 10-60 minutes, and standard is from >30 minutes.
Is that regardless of increment?

@CheesyPuns: ok, but how do we factor in a time increment? I think a certain number of moves is assumed, multiplied by the increment and then added to the base time, question is what is that number of moves?
>rapid is from 10-60 minutes, and standard is from >30 minutes.
So 45 minutes would be both "rapid" and "standard"?
Furthermore, I think that the game setup dialog should make it explicitly clear which category the game is going to be belong to. With no increment it may be easy to figure out, but with increments it's not obvious anymore, especially that the formula for calculating the total time of an increment game doesn't even seem to be widely known, as per above.

I answered to CheesyPuns (Other was meantime discussing). He said ", and standard is from >30 mins."

I answered to CheesyPuns (Other was meantime discussing). He said ", and standard is from >30 mins."
He said in OTB play standard was >30 mins. He gave a different bracket for chess.com.

>increment is added in minutes
That would imply assuming of 60 moves per game (which incidentally causes every increment second to become a minute in total).
>or completely ignored
Whoa, it's a huge difference whether you add it (as per the above), or ignore it. For instance, a 2|15 game would be considered a 2min bullet game if the increment is ignored entirely, and a 17 minute rapid game with the increment being accounted for (with n=60).

Most chess sites, I believe, consider blitz as all moves for one side are less than 15 mins. (with bullet as those under 3 mins.) and if an increment is used, figure 60 moves, or 1 min. per increment amount, to determine the increment total time to add to the fixed time. (I've found 40 moves to have been used also.) The USCF, however, considers blitz as under 10 mins.
Simple question. Is it only 1 min? Or is 3 min too? 5 min? Is 10 min stil blitz?