These words are used interchangeably, but to discriminating users of language a longshoreman (the word longshore is a variant of alongshore) is someone employed to load and unload vessels. A stevedore (a word derived from a Spanish term meaning "to pack," "to stow") is an employer of longshoremen. A stevedore is a hiring firm or group of men; a longshoreman is a laborer on wharves.
Dictionary of problem words and expressions. Harry Shaw. 1975.