My international students almost always say "revise" when an American student would say "review."
The both come from the same roots which mean: "Look again,' and I bet that is how this overlap in meaning came about.
In American English, "review" means to go over the material again, to practice it once more, to repeat what has been learned, to refresh your memory of the material.
But "to revise" is to edit a written paper in order to correct and change it.
Before a test, American students review the material.
But they get back the first draft of their term papers with the Professor's advice to revise their work -- to change it so as to edit out its errors.
Student or Learner