How a certain bpm(say 120) interacts with certain timestamp(say 4/4)? Are all timestamps at the same BPM? Is BPM and tempo are the same thing?
It's not a time stamp, it's the time signature (or meter). It tells you how long a measure is and what gets the beat. In 4/4 time, a quarter note gets the beat and four of them make up a measure. In 3/8 time, an eighth note gets the bar, and three of them makes up a measure.

BPM is beats per minute. It indicates the speed at which a song is played. The "beat" is what the time signature tells you gets the beat. (Quarter notes in 4/4 time, eighth notes in 3/8 time).
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I've got my thick skulled drummer head on at the moment so here goes..

I think i know what you're getting at, and im going to go out on a limb here and assume that you are composing with midi of some sort and getting screwed over by triplets,
but no they dont interact with each other like that at all. Tempo and bpm are just tools for notation. literally the briefest outline of the rhythm for the song. those numbers are mostly just for notation.

bpm is like your constant, the time signature is a guide for how you are supposed to divide up and accent the constant.

120 bpm is the same speed in 4/4 as it is in 3/4 and or 5/4 or whatever. Get a 1/4 click track at any tempo and count an x/4 rhythm over the top.

like, 1, 2, 3, 4 for 4/4

or 1, 2, 3 for 3/4

or 1, 2, 3, 4, 5 for 5/4

a bar of 3/4 rhythm will take up less actual time to play, and 5/4 will be longer, but the speed is the same because the length of a minute isnt changing any time soon.
60 seconds of music at 60 bpm will have 60 beats, regardless of how they are split up.

if my midi or computer composing guess was even in the right ballpark then your confusion might possibly be coming from writing something which is technically still in 4/4 but you are using triplets to get a 6/8 or 12/8 feel which gives that dubstep shuffle feel.
If you want to play a 6/8 rhythm (1+a 2+a...)over a 4/4 beat (1+ 2+...) then you would have to stretch that rhythm so it fits nicely in the bar. If you were actually writing that rhythm in 6/8 rather than just in 4/4 using triplets, then yes, 6/8 would have to be written as being three quarters of the 4/4 tempo.

this all really only matters for notation.

hope any of that helped.
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