The other answers are correct. In addition, both words can be nouns and verbs. “Jump” is more common as a verb. “Leap” is more common as a noun.

Greg said it well, I will add in context "leap" is a kind of "jump". So everywhere you can say "leap" you can say "jump" (it works both ways theoretically but "leap" will always be more exagerated). "Jump" is more prominent in general. The only example I can think of where "leap" is used extensively (but not exclusively) is with frogs. Frogs "leap" (also frogs "jump")

'Leap' is similar to 'jump', but with 'leap' you go higher and further. When I think of 'jump', I think of bending my knees and making a strong effort to push myself off the ground. If I made this same effort with a 'leap', I imagine myself going far higher and further and with a sense I was lighter than what I really was. That is, I go further as if my weight and gravity weren't holding me back as much as when I 'jump'.

Thank you!

Literally speaking, leap is a long distance and jump is a short distance. Jump can also just be up and down without moving forward (such as "jump up"). Figuratively speaking, they may be used in different situations. We say "make the leap" or "take the leap" to mean make a big change that may be scary. "Take a leap of faith" is similar but it means to trust someone/something when you do something scary. We don't use jump in these phrases. But we do say "jump to conclusions," which means to assume something is true even if you don't have enough information about it.