Naval diving is Navy or Coast Guard (or Army underwater construction) diving done by hard hat divers to repair ships, salvage, do dock maintenance, etc. It is not "all diving done by Navy personnel". They're ND ratings, and while technically part of Naval Special operations, not SEALs. There are probably some special missions where Naval divers have done something special opsy (tapping undersea cables, or salvaging a foreign nation's warship without their knowledge or consent), but it's not routine. Naval diving techniques are basically adapted commercial techniques, and in a lot of cases are more conservative and safer than what cheap commercial contractors use.
SEALs are probably never qualified Naval divers, unless they start out as Naval divers and then switch to SEALs.
What SEALS do -- Combat diving, combat swimming, etc. is called "military diving". That tends to be dangerous, although not as much due to the diving aspects (it's a lot of oxygen or other rebreather use at shallow depths, undersea scooters for long transits, etc.), as due to the other people trying to kill you. Also, at least recently, SEALs mainly engage in combat on land in countries with no contiguous oceans :)
SEALs are probably never qualified Naval divers, unless they start out as Naval divers and then switch to SEALs.
What SEALS do -- Combat diving, combat swimming, etc. is called "military diving". That tends to be dangerous, although not as much due to the diving aspects (it's a lot of oxygen or other rebreather use at shallow depths, undersea scooters for long transits, etc.), as due to the other people trying to kill you. Also, at least recently, SEALs mainly engage in combat on land in countries with no contiguous oceans :)