The way I understand it, an acronym is the initials of words used to shorten a long phrase, like CIA, FBI, BBC...
An anacronym is one such phrase shortened to its initials that are no longer in use, or that people don't remember.
Anachronism, however, is an historically incorrect phrase or thing, like when an actor wears a wristwatch in a medieval movie.
A pseudonym is just another name for something or someone, like when authors write under a fake name.
Does any of this make sense? lol