You said 'I thought the weapon had to have 'GRA' next to it, but that wasn't the case for all the weapons I've used mods on.' This implies that you are trying to interchange GRA and none GRA. I have not heard of this before I would make certain that before you buy any GRA mods the weapon you are buying it for has GRA in it title. You have GRA weapons and you have all the other none GRA weapons they should not be interchangable from a mod standpoint normally.
No GRA parts should work with a none GRA weapon either. Well there are no gun runners Laser rifles only a tri beam so if you buy parts for a Tri Beam laser rifle added in by GRA they wont work on a regular laser rifle.