A burglarer is an obsolete term for a person who burgles someone else.
There is no common term "burglarer." It could be a misspelling or misuse of the word "burglar," which refers to someone who breaks into a building to commit theft or another crime.
A burglar is a person who steals items from another premises.
A burglarizer is a rare term used as a synonym for a burglar - a person who steals property from a location without prior permission.