They would rarely be interchangeable, even though they are very close in meaning. A jump, implies a single movement, from one location to another. It is implied that the person jumps because it is not possible to walk or run from the first to the second point. 'He jumped from the balcony on the first floor' Skipping is an activity of children. It actually describes two activity. One is a cross between running and hopping, that is very difficult to describe in words. But the child bounces from one foot to the other, shifting their weight. The second skipping activity is when a child is jumping over a rope, that two other children are swinging. Skipping has other meanings - skipping stones - throwing a flat stone so that it bounces on the surface of water - I skipped class - I avoided my class and did something else for the time - my music is skipping - there is a scratch on my cd / record and it does not play smoothly. Hopping is like the first skipping. However, if an adult hurts one foot and must cross a room using only one leg, they are said to 'hop' across the room. It is the action of a rabbit or a kangaroo when they move on two legs at the same time. Another synonym is 'leap' which is like Jump, only it implies that the person jumped as far as they could possibly jump.