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I've recently watched a BBC documentary about the history of music and recall an episode where they talk about music that has two distinct tempos (and possibly time signatures) at the same time for different sets of instruments.
Still, I can't remember how this is called and who are the famous composers that composed that way (Stravinsky?).
The answer here is deceptively simple: Polytempo. There are other names, such as multi-tempo, polytemporal, and others, but they all describe the same phenomena.
Here is a link for further reading on Wikipedia.
For a list of composers that have used this technique, as well as the pieces in which this technique was used, check out this page and look under "Compositions".
I want to clarify for everyone that Polyrhythm and Polymetric are both incorrect here. Polyrhythms are multiple, independent rhythmic lines (typically ostinatos) that can form a hemiola or hemiola-like effect in music. Polymeters are ways of organizing the beat. Tempo is the speed of the beat, not how it is organized, or the rhythms that it defines.
Here is a wonderful Q/A from this very website that addresses the difference: Polymeter vs Polyrhythm
This sort of thing has been explored pretty deeply by, among other people, Conlon Nancarrow. He used player pianos to perform pieces which would most likely have been too complex for anyone to perform organically. One way in which he complicated things was that he used what he called a tempo canon. As discussed here, one such piece was his Study for Player Piano 41a. It used multiple voices, each with its own tempo and the ratios were on a strict, but irrational ratio. If the ratio between tempos was rational, it would line up, or converge, so that two notes could fall at the same time. However, if the ratio was irrational, they would never converge and dance around each other until the piece ended.
This basic concept, although the effect can be jarring, is really not very different from polyrhythms and polymeters. It's just obfuscated by using complicated ratios. For example, if you have a bar and a main voice hit four evenly spaced beats, you have the standard quarter note pulse in 4/4. You can fit 3 notes evenly into that same bar in a second voice and the second voice will be playing half-note triplets. For every four notes in the main voice and every three notes in the second voice, the voices will play together. That's your bar. And that's a polyrhythm. That would be a 4:3 ratio. I'm not sure that's how it's typically notated, but the idea translates. You can imagine how this can be seen as two voices at different tempos. Say maybe one voice in 4/4 at 120 and another voice in 3/4 at 90. They would line up the same way.
Here's another example. If your main voice plays 8 eighth notes before repeating and your second voice plays 7 eighth notes before repeating, they will line up every 56 (7×8) eighth notes. In other words, after your main voice repeats seven times and your second voice repeats eight times. That's a polymeter. Now you can see how these concepts can get mixed up. As the ratios get more complicated (ie 128:73) or less rational (ie √2:φ), the tempos line up less and less and the individual tempos will get closer and/or less distinguishable. That is where you cross the line into tempo canon territory.
Note: I understand that 'irrational ratio' is a terrible oxymoron, but I can't think of better terminology. Also, this is just the one conceptualization of the multiple tempo idea. There is world music where this is done organically and many people have already mentioned other composers who have worked with the idea. But hopefully this helps.
There is both polymeter and polyrhythm.
Polymeter is sometimes referred to as "tactus-preserving polymeter." The measure size differs, the beat is the same. Since the beat is the same, the various meters eventually agree.
https://en.wikipedia.org/wiki/Meter_%28music%29#Polymeter
A good example of polymeter is the Tala which is an extream form of complex time.
Polyrhythm is the simultaneous use of two or more conflicting rhythms, that are not readily perceived as deriving from one another, or as simple manifestations of the same meter. The rhythmic conflict may be the basis of an entire piece of music (cross-rhythm), or a momentary disruption. Polyrhythms can be distinguished from irrational rhythms, which can occur within the context of a single part; polyrhythms require at least two rhythms to be played concurrently, one of which is typically an irrational rhythm.
https://en.wikipedia.org/wiki/Polyrhythm
Commonly used in modren Jazz. See: Mongo Santamaria and Elvin Jones.
Neilsen's 5th symphony was an early example (1922). Towards the end of the first movement, the side drum part is in a different tempo and time signature from the rest of the orchestra. The first edition of the score instructed the drummer to "improvise as if at all costs he wants to stop the progress of the orchestra".
In a later edition that instruction was replaced by a written part which breaks off with the direction "cadenza ad lib".
Skip to about 14:45 here:
(There is also an important side drum part in a more "conventional" rhythm earlier in the piece.
