From Liquipedia StarCraft Brood War Wiki

A match-up (often abbreviated as "mu") refers to a StarCraft game's defining characteristics. This may include any combination of players, races, and map. Race match-ups are abbreviated PvP, PvT, PvZ, TvZ, TvT, and ZvZ.

The difference between PvZ and ZvP is the perspective. If Bisu is facing Jaedong, Bisu plays a PvZ while Jaedong plays ZvP. Although there are only 6 match-ups from an observer perspective, a random player has to master 9 match-ups because of this perspective reason (you would count ZvP & PvZ etc.)