They're the same in meaning, but "oft" is an older, more cerebral usage, and as far as I know it comes from German ("oft" in German too). Your average person won't use it but "educated" people would (or should) understand.

Oft is rarely used in conversation. It shows up in poetry and some older writings most often. The usage would be as a prefix to discribe something as happening often such as "oft-remember" "oft traveled". It would be incorrect if used like "Yes, I go to that store oft." You can go your whole life and never have to use it, but you may see it writen, when that happens the meaning will be clear.

"Oft" is old, poetic and eloquent, so don't expect to use it in daily speaking and writing. You'd apply it to keep a poetic rhythm, the same as how we've shortened "over", "ever", "of the", "in the", etc, down to a single syllable: o'er, e'er, o'th', i'th'. It's also used as part of a compound expression, but still eloquently/poetically: "oft-expressed philosophy" "oft-repeated tales" (note the even strong-weak rhythm in both phrases).