When speaking of hypothetical tech. the author is free to use words poetically. There are some common clichés that are used:
quantum leap In science, the smallest possible change in energy levels. Use metaphorically to mean a sudden dramatic change. Used in the sci fi to mean a sudden change in time and space, most notably in the Quantum Leap series.
Jump to hyperspace the "hyper" prefix is used in mathematics to indicate a higher dimension shape, such as a hypercube. In sci fi, making a hyperspace jump suggests traveling through a higher dimension. You'll also hear "jump to lightspeed", a sudden acceleration of a spacecraft to magically high speed. These hyperspace or lightspeed journeys are often not instantaneous.
Hop suggests something smaller than a jump. It might mean that the space craft disappears from one location and reappears in another instantaneously. Players of the 80s computer game Elite will remember that one could use hyperspace to travel from one star to another, then having arrived at a star, one could make "interspace hops" to rapidly approach the planet.
Bound does mean "jump" (From French bombir, originally meaning make a loud noise, ult. from L. bombus onomatopoeia for "buzzing") but it also has another meaning (from Norse búinn=prepared), which means "Moving in the direction of". It is this meaning when we say "Bound for the planet", Its not about jumping. (Bound has two more unrelated meanings, boundary and the past participle of bind. 4 homonyms!).
Spring: I can't recall this words being used in this context, though no doubt there is some author who has.