Чем отличается skipping от других видов прыгания, меня как-то не волновало. А вот разница между hop, jump и leap - вот это любопытно. И главное - умудриться запомнить. Опять же, американцы утверждают, что:

"to jump" or "a jump" refers to the generic act of exerting with one's legs the force needed to leave the ground. It could be straight up or it could be with horizontal momentum (i.e., "the track athlete took a running jump to get over the hurdle").
Примечательно, что есть и фраза "jumping up and down" - jumping in one spot (as in excitement). Наша любимая Peppa Pig loves jumping up and down in muddy puddles.

"to hop" or "a hop" makes one think of a smaller jump, like that of a rabbit or a small child. The phrase "bunny-hop" refers to jumping short distances with your feet together (like a rabbit).
Здесь дама из Лондона вносит дополнение: Hop - сan also mean jumping on one foot.

"to leap" or "a leap" has a bigger feel to it than a simple "jump." Leaping suggests distance (i.e., "the deer took a mighty leap and made it over the river.")