The term master has different meanings.
A master is a dominant, but the term implies a more pervasive relationship than "dominant" does. A master is usually a master to a specific other person or persons. A Master/slave relationship suggests one that goes beyond sexual scenes, affecting the day-to-day life of the people involved.
However, different people have different conceptions of the role, and may use it in different ways. There is no single accepted and definitive list of traits that a "master" must possess, nor is there clear agreement on what distinguishes a "Master" from a "dominant".
The term "Master" may be used as a term of address, either alone ("I wish to speak with you, Master") or prefixed to a name ("Master Michael").
In non-BDSM contexts, a master may be a person who has achieved a high level of skill is some trade, craft, or profession (such as a "Master plumber", "Master carpenter" or "Master musician"). In this sense it evokes the guild organizations of the Middle Ages. Such a master is permitted to train apprentices.
In the 19th century, boys under 13 years old were addressed as Master; boys between 13 and the age of maturity were not accorded any courtesy title; and from the age of maturity on, they were called Mister. For example, in the spanking novel The Old Rectory, the 12-and-a-half-year-old Henry Perceval is addressed as "Master Perceval", even when he is being reproved and punished.
Also some what archaic English, Master is the male equivalent of Miss, reserving Mister for married men.