They are both OK and mean the same thing. To jump out is to jump from inside something. To jump off is to jump from on something. With a tree, it's the same thing. (as being on a tree branch is also being in a tree) If it was a building: To jump out of a building = jump from a window To jump off a building = jump from a ledge (maybe window ledge) or from the roof Another example of when it's the same: Jump [out of / off] a train. Because if you are IN a train you are also ON a train. If it's from the roof (or some other exterior) of the train, you can only use "off".