Although some people have referred to the Time Lords as a race, that is not true. All Time Lords are Gallifreyan, but not all Gallifreyans are Time Lords. Only after graduating from the Academy on Gallifrey does one become a Time Lord.
..at least, that was the case up until the revival series. In recent years, the waters have been muddied considerably, most notably in "A Good Man Goes to War" when reference is made to Time Lord DNA and the River Song being part Time Lord; and before that, Jenny, the Doctor's "cloned" daughter in "the Doctor's Daughter" is also described as being Time Lord. Both, along with the incident of Donna Noble becoming the DoctorDonna in "Journey's End" use the term in the context of a species, not an occupation or a title.