Sub (short for submissive) is a term used to conote a person who gives up control and gets satisfaction from aspects of submission which may include serving or being used by a Dom or dominant person. Subs often are turned on by suspense, vulnerability, and/or giving up responsbility. They don't dictate the scene except in very general terms. Such a person could also be a masochist or bottom but this is not always the case.
The relationship between a sub and their Dom may be very transitory or can be permanent. Some subs are married to their Dom. Long term relationships are known as D/s (Dominant/submissive) relationships.
People are clearly entitled to call themselves whatever they want and the term sub or submissive is sometimes mixed up with both bottom and slave. Indeed, a Bottom or a slave may well be submissive.