The main distinction is between Polyrhythms and Polymeters. The two are often confused.
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. (Four measures of 7/4 = seven measures of 4/4).
Polyrhythm is sometimes referred to as "measure preserving polymeter,". The beat varies and the measure stays constant. E.g. in a 4:3 polyrhythm one part plays 4/4, the other plays 3/4, but the 3/4 beats are stretched so that three beats of 3/4 are played in the same time as four beats of 4/4.
More generally, sometimes rhythms are combined in a way that is neither tactus nor measure preserving - the beat differs and the measure size also differs. See Polytempi.
Research into the perception of polymeter shows that listeners often either extract a composite pattern that is fitted to a metric framework, or focus on one rhythmic stream while treating others as "noise". This is consistent with the Gestalt psychology tenet that "the figure-ground dichotomy is fundamental to all perception" (Boring 1942, 253; London 2004, 49-50). In the music, the two meters will meet each other after a specific number of beats. For example, a 3/4 meter and 4/4 meter will meet after 12 beats.
In "Toads Of The Short Forest" (from the album Weasels Ripped My Flesh), composer Frank Zappa explains: "At this very moment on stage we have drummer A playing in 7/8, drummer B playing in 3/4, the bass playing in 3/4, the organ playing in 5/8, the tambourine playing in 3/4, and the alto sax blowing his nose" (Mothers of Invention 1970). "Touch And Go", a hit single by The Cars, has polymetric verses, with the drums and bass playing in 5/4, while the guitar, synthesizer, and vocals are in 4/4 (the choruses are entirely in 4/4) (The Cars 1981, 15). The Swedish metal band Meshuggah makes frequent use of polymeters, with unconventionally-timed rhythm figures cycling over a 4/4 base (Pieslak, 2007).
Read more about this topic: Meter (music)