Well, I don;t really know what it's called. All I know is that it shows up on the loading menu by itself and in an elf''s hand sometimes. The sword is black with some red lines in it. It looks daedric to me but it's not one of the artifacts.
The one the dunmer is holding is actually a daedric dagger. The one that has a blade with a split along it is the daedric longsword. You can make them with smithing, or find either as loot (tho likely only at high level, its an endgame unenchanted weapon type).
Daedric weapons are separate from daedric artifacts. The former is a type, like steel or orcish. The latter are each unique and unforgeable, since they are made from the blood of a daedric prince.
The unenchanted daedric weapons are forged from ebony and daedra hearts.