Several of the Weapon Training Skills list SP weapons as one of the types, but I can't figure out what that stands for.

It stands for Self Propelled, aka: bullets and shells.

Thanks, Boss.

That could have been made more obvious.

Would that include ships' cannon if you have Heavy Weapon Training (SP)?

First of all - it's not Self PRopelled, it's Solid Projectile. But yes, it's bullets and shells. Revolvers, machineguns, shotguns etc. But bolt weapons are separate class of weapon.

And you don't need any weapon training to use ship's weapon. You only need good BS.