What's the difference between a Dominant and a Master?

Scope and duration. A dominant leads a scene or an encounter. A Master or Mistress holds authority that continues when the scene is over, and usually when nobody is watching.

The Master/slave world is the most heavily negotiated corner of this vocabulary, often with something written down. What's being agreed is not an evening but a structure two people live inside, which is a considerably larger thing to take on.

Neither is a rank. A dominant is not a trainee Master, and plenty of people who lead brilliantly for an hour have no interest at all in running someone's week.