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There are three types of drives used in spacecraft.
Sub-atmos Drive
Technically not a starship drive, but they are fitted in some starships that require access to planetary atmospheres. Typically these are older ships, or ones built on the cheap, as modern ships have incorporated sub-atmos drives into their stardrives.
Stardrive
The stardrive was whe first ship drive that allowed interplanetary flying. This tek has developed a lot over the last couple of millenia, and modern stardrives often incorporate sub-atmos drives.
Modern stardrives are powerful enough to allow ships to cross multiple galaxies, but the time in which they do it, and the fuel needed to do it make jumpdrives more economical in the long run. Of course, there are people who can't afford a jumpdrive -- or a ship big enough to mount a jumpdrive -- and so will make one-off long trips using their stardrives. They do, however, have to make regular stops to refuel and to get more food.
Stardrives use known spacelanes to make short jumps with maximum safety because they're stupid and can't adjust course. These spacelanes are common trade and travel routes.
Jumpdrive
The ultimate in drive tek. The Jumpdrive allows a ship to travel across the universe in very short times.
A jumpdrive is effectively a wormhole generator. It creates a tunnel of pressure with negative energy around the ship. Gravity generators at the bow and the stern create the mouths of the wormhole and are constantly moving as the ship moves forward. The tunnel, or throat, of the wormhole surrounds the ship itself, so as the ship is propelled forward the wormhole moves with it.
The narrower the throat, the faster the ship can go. This means that larger ships can't go as fast as smaller craft because with more mass, the wider the throat has to be. A wider throat results in less pressure to propel the ship.
If the grav generators fail, the mouth of the wormhole closes, and well, nobody has any idea what happens after that. There are several theories from disintegration to lost-in-space, but naturally, experiments haven't been able to prove or disprove anything. Disintegration is the most popular theory, but even that is segregated between immediate painless disintegration theorists and the relatively quick, but utterly painful disintegration camp.