Sorry, I'm new to this (and speedrunning in general).

What is a cycle in MM, and how does that differentiate from splits?

When people say a cycle, we're talking about a 3-day cycle in Majora's Mask. You start a new cycle by playing the Song of Time to warp to the start of the 1st day.

A Cycle is a 3 day period. When you play the Song of Time, it starts a new cycle.

A Cycle (speedrunning in general) is an action that repeats itself consistently. 3 day period is called cycle because once it passes, you go back again and start new 3 day period from Clock Town