I use chevrons (⟨⟩) to denote the concept behind the word.
[ Source :] Meter is the rhythmic structure of the music. For example, a piece of music could be in 4/4 meter, which is a strong-weak-medium-weak pattern of beats. It could be in a compound meter, where the notes are subdivided into three instead of two. It's a general structure that the music fits in. Not all music has this!
Rhythm is the actual timing of the music (relative to the tempo, I guess). For example, a rhythm for one measure of 4/4 might be a half note followed by two eighth notes and a quarter note. You can have many different rhythms within the same meter! This measure may just have a whole note as its rhythm, while that other one might have eight eighth notes.
Why was 'meter' chosen as the root in ⟨polymeter⟩ and 'rhythm' in ⟨polyrhythm⟩? In other words, why wasn't ⟨polymeter⟩ called polyrhythm instead, and ⟨polyrhythm⟩ polymeter? I understand the choice of 'poly-'.