A gangster is a member of a criminal gang. Gangsters are sometimes called mobsters.
A gang is a criminal organization, and a member of such a group is a gangster. Gangsters work together to commit robberies and break the law in other ways. Many famous movies, such as The Godfather, are about gangsters. This word often refers specifically to members of criminal gangs of the 1920s and 30s, when organized crime frequently involved the smuggling of alcohol.