Wow was slow speed variations (under 4Hz). Flutter was quicker warbles.
Both were caused mechanically. The rubber wheel - pinch roller - that moved the tape might not be perfectly circular, the motor that pulled the reels might be uneven, and the tape case sometimes pressed on the tape reels causing variable friction.
Analog media really were a bit crap. I get the creative distortion idea, but even so - ewww. I'm so happy these kinds of imperfections are optional now, and not baked into music distribution systems as an expected flaw.