How does a Black Soul Gem differ from any other soul gem? I have one with a grand soul in it, so clearly it can take Grand souls. And because soul gems can take souls that are smaller than the container, what is the classification "Black" for?
Black Soul Gems are exactly like Grand Soul Gems - with one significant perk:
They can trap humanoid souls.
Regular soul gems are restricted to creatures and undead only.
But black soul gems?
Tired of the blacksmith sending out hits on you? Kill him, trap him in a black soul gem, enchant him into a ring, and then sell the ring back to his wife. Justice is served!
Black soul gems are essentially grand soul gems that can trap or store the souls of humanoid (player) races. If you dont have an empty black soul gem in your inventory when you kill a humanoid NPC (like a bandit or imperial soldier) that you have applied the soul trap effect on, you get the "you don't have a soul gem in your inventory capable of holding such a soul" (or equivallent) message. When you have an empty black soul gem in your inventory you capture the soul instead.
They can be used at an Atronach Forge to make Daedric weapons and armor.