I didn't realize it before, but that laser musket is literally duct-taped together.

It has the same laser head core. If that is what people are considering the basis of a base weapon, they are similar. The fact that we shoot a red laser should be indicative that we are using the same laser head; the light's wavelength is the same as other laser weapons.
Instead of a place to load energy cells, there is a crank case, probably geared and linked to a rotor/stator set up that gives us our charge. Until we get any info on them, the stock and grips being wood and the barrel being different is fairly cosmetic, IMO. At the end of a day, it's a laser weapon.

If we are considering everything laser we see in the video to be a laser base weapon, then I think it's safe to put the musket in the same group.
Focused and scatter shot mods are as much as or more of a variant as far as the end result goes than the laser musket, I'd say.

What if the base weapons don't break down into anything organized, and vary on a case-by-case basis? It can't be completely based on how the weapon handles, since you can turn Laser, Plasma, or Pipe guns into rifles or pistols. It can't always be based on ammo type, since the Pipe Gun can be modded to receive different ammunition. And it doesn't seem like every gun can be transformed into something radically different - we didn't see any mods on the Assault Rifle that would change it to a pistol, or a non-assault weapon.

Two very different and equally valid viewpoints here, and I like the thought process behind both. It will be interesting to see just how the various weapon types end up being categorised in the final game, but I have no doubt that the system will feel complete and highly intuitive once we get to try it out for ourselves.

I don't think we need to worry too much about weapon awesomeness in this game. If it's 50 base weapons + all the different mods AND probably unique weapons, I think I'll be a very pleased wasteland explorer

Yet we seen the assult rifle semi fire.

That may have been due to the player tapping the button rather than holding it down rather than because the assault rifle was modded (or starts out as) being semi-auto fire.

I think the only thing that separates 'base weapons' are what mods you can apply to them. The laser musket doesn't look like it can take all of the same mods as the laser pistol, so it's not the same base weapon. The laser rifle can take all the same mods as the laser pistol, so it is the same base weapon.

Consider full auto is a mod, it's not to far fetched to assume it can be replaced, so I'm more inclined to see it as semi auto fire.