I see that the prospector's axe states using the D8 for hit. Does that mean the damage is a D6 rather than D8? It reads differently than the shotgun.
Yes. Any weapon that uses a die different than a D6 is specifically detailed by the weapon. The shotgun says D8 for hit and damage. The Prospector's axe say D8 for hit. The Trun Disintegrator says 3D6 for damage but nothing about to hit.