The gift itself is inborn. The ability to express it is learnt and trained.

For me, It's a combination of both. When someone "performs" ( what kind of performance are we talking about? ) in a excellent way it's because of the function of his experience/acquired skills and his natural talents. If you have a "gift" -thanks to Mother Nature- you should refine it. =) But this doesn't mean you can't do everything in your hands to become GOOD at something (by learning, practicing and giving your 100% ) even if you think, you don't have the innate talent. ^^

both i believe.... you may have a beautiful voice or convincing acting as an inborn skill or you can practice and work hard to achieve it .

Ability will acquire part of the progress ...

If you are talking about a musical performance then I think it is both. Musical ability tends to run in families.