What's the difference when it comes to studying?
I agree, and we should perhaps specify that British speakers call it "revising for" a test.
Note that review has other meanings in AmE as well: to study for a test seems more intensive than to review, which sounds like "go through once more" to me. Also, to review can mean to read and then write an opinion about what was read.
In American English they are different.
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.
This was a big surprise for me in 1984, when I started writing at what was then the Digital Equipment Organization. I had to release a draft of what I was writing 'for review'. In my experience, a review of written work was like a published book review - along the lines of 'Absolute rubbish, a school-leaver with a word processor could have done better. Are we paying Mr Knowles?' By the time I left the company, I was speaking the language like a native!