Concealed Weapon can include knives, Tasers, etc. In states that issue Concealed Firearm Permits and Concealed Pistol Permits (with "Pistol" or "Firearm" in the name), they often prohibit the concealed carry of any other weapon -- lethal or not.
Same for states that choose to omit "Concealed." Indiana, Pennsylvania, and Minnesota are Permit to Carry states which means, you can choose to have your gun fully concealed or carried in plain view. Others call this LTC or License to Carry.
It's all a state-by-state situation. Know the laws of each state in which you can carry. This is especially true if you are using CCW Reciprocity. Your License to Carry might allow open carry where it was issued, but it might only allow concealed carry in states honoring that issuing state's permit.