Practice is more like εξάσκηση. Μια πρόβα-a rehearsal is a kind of practice. But a band member is practicing on his own, and is having a rehearsal with the other band members. It's not exactly the same thing. ;)
And yet, throughout my school days, I can remember kids saying, "I've got band practice this afternoon."
Is this related to "prove" in the sense of test or try?
They have the same root. Προβάρω and prove both originate from the Latin probō. ^.^
(Probus in Latin means good, excellent, so the verb means something like to try to be good.)