Does fukushuu suru mean "to review" or "to revise"? Which meaning may be closer to actual usage?
It means review.
to go over (lessons, studies, work, etc.) in review.
It also means revise, if you are going by the British English definition.
British. to review (previously studied materials) in preparation for an examination.
It can also mean "(exact) revenge", but it uses different kanji.
As an addendum to Amani's post, it looks like this fukushū reading has four possible spellings and three meanings -- three spellings with verb senses, and one proper noun: