In common usage, a starship is a space vessel capable of interstellar travel under its own power.
Star Trek seems to use the term a bit differently. In TOS, a plaque on the wall of the Enterprise's bridge identified the ship as a "Starship-class" vessel, and some episodes have implied that in the Federation, the term is reserved for Starfleet vessels.
Certain trekkies have attempted to argue that the Death Star is not a starship, basing the claim on its poor maneuverability, "low density" of weapon mounts, and low thickness of armor relative to its diameter. Why they would make this claim when it is obviously capable of propelling itself from one star system to another is a mystery. The listed attributes have nothing to do with the feature that distinguishes it as a massive starship, its hyperdrive.
- TNG "Angel One"