The types of damage I know:
– Physical (attacking with a weapon)
– Physical Elemental (e.g. Liquid Steel)
– Magical (e.g. Black Sky?)
– Magical Elemental (e.g. Firaga, Holy)
– Magical Non-Elemental (e.g. Ultima, Flare)
– Elemental (e.g. Fire Gem, Shadow Gem)
– Non-Elemental (e.g. Shining Gem, Supreme Gem)
Since the description just says "major damage" and not "major non-elemental damage", I just assumed it was some other type of damage.
I guess Black Sky would be magical non-elemental then…