The Jump Drive works by temporarily opening naturally occuring wormholes that connect nearby stars to each other. Presumably, these wormholes are a natural byproduct of the way that massive objects bend space around themselves under General Relativity. Passing through one of these wormholes (commonly called Jump Points), is virtually instant, allowing one to cross several light-years (or an entire sector as is the case with the Enigma Black Hole) in a moment, but one can only travel to a system if one goes to a preexisting Jump Point that leads there. Of all known races, only the Steltek are capable of generating new jump points at any time and place, although the Nephilim wormholes can produce a similar effect in places where the conditions are favorable.
The Hopper Drive, by contrast, creates short-distance single-use wormholes through which a ship can travel. The wormholes can be generated to take a ship in any direction, which allows faster-than-light travel to areas far distant from Jump Points, but this type of engine has two drawbacks. First, the distance for a "hop" is fixed by the engine--you cannot choose to hop over a shorter than normal distance to get the drop on an enemy, for example--you must instead hop as close as possible and then spend hours cruising toward the target under normal drive. The second drawback is that the Hopper Drive leaves residual radiation when it is used, so it cannot be engaged again until the radiation has disappated, which can take a couple of hours. Thus, the Hopper Drive cannot be counted on to allow you to hop away from an enemy if you have just used it recently.