The vast majority of vessels smaller than capital ships make use of ion drives and monopropellant cold gas thrusters (hydrazine is still popular) for maneuvering and travel within a local system. Vessels limited to these systems aren't generally considered interplanetary vessels, although there are a few exceptions such as the First Wave generation ships. To be designated an interplanetary craft, a ship must either possess a gravity drive or have the required field surfaces to ride along in the wake of one.
Gravity drives, officially termed 'Alcubierre drive-derived wave inception systems', generate distortions in local space-time that allow the spacecraft to 'surf' along them. Don't think about it too hard or it will turn out to be made of handwavium and tissue paper. The first mark of drive, developed in the 2100s, could get a ship up to around 0.01c and the current mark III drive, in use on cutting-edge military ships, can hit 0.03c.
All but the very oldest ships with enough power capacity to make use of a gravity drive do so. The power requirements for this kind of propulsion are immense, but do not need to be sustained. The size of the wave is proportional to the amount of power supplied to the drive; multi-kilometer vessels, or massive stationary facilities fed power by huge solar arrays and fusion plants, are the general minimum size to power the wave inception system, although smaller ships are able to ride the disturbance generated without expending much power. Because of this, fleets tend to have a primary gravity drive in the flagship, with the smaller ships equipped with much slower standard drives.