When it comes to weapons, it looks like three main types: beam weapons, kinetic weapons, and missiles. Beam weapons are lasers and particle beams. Kinetic weapons are coilguns, railguns, and shrapnel weapons. Missiles are, well, missiles. Ken Burnside compared it to a policeperson armed with a service revolver, a shotgun, and a police dog. The revolver (beam weapon) cannot be dodged or outrun, but can miss. The shotgun (kinetic weapon) is more likely to hit, but with reduced lethality. The dog (missile) can be dodged or outrun (or shot, that would correspond to point defense), but the blasted thing will chase you, and will always hit unless you actively prevent it.
(Holger Bjerre begs to differ. He points out that kinetic weapons are less likely to hit since it can be dodged, beam weapons lose lethality with range just like shotguns, and kinetic weapons do not lose lethality with range just like revolvers. Well, no analogy is perfect...)
Dave Bryant has his own analysis of spacecraft weaponry here. I'm not sure I agree with all of it, so do your own research.
These are preliminary classification schemas offered "as-is". Tinker with them to suit your taste.
This scheme was created by Erik Max Francis, and contains some modifications by Isaac Kuo:
This scheme was created by Timothy Miller (Cerebus), and contains some modifications by Erik Max Francis: