From my experiences, yes, they do have a randomized set of characteristics, based around a central theme.
Is generally boxy, and will have a raised cockpit. With some symmetrical wings, or thrusters. I usually find these in Vy'keen systems.
Is usually based around a central sphere like cockpit and will have odd looking bits attached and will not be symmetrical. Usually a Korvax ship.
Long and flat, usually with two cylinders on each side. Find these most in Gex systems.
Usually a 'pointy' ship, so will be flat, with a pointed cockpit and symmetrical wings.
I think these are randomised, as my ship is just a small sphere with two large vertical fins, and is not classed as any of the above.