Psychological egoism asserts that all individuals have a single objective: his own individual self-interest or welfare. It therefore follows that if an individual prefers comedies to horror films, he will maximize his own welfare by watching more comedies and fewer horror films.
Ethical egoism claims that not only do people look out for their own self-interest, but that it is morally right to do so, and that they do not have any moral obligations to others.
Rational egoism argues that it is always reasonable for an individual to promote her own self-interest. This form of "ethical selfishness" was propagated by Ayn Rand in her book "The Virtue of Selfishness," and dictates that an individual's own interests should always determine her own actions.
Egotists are people who are selfish and conceited in that they exaggerate their own personal characteristics and value.