I agree. We have to be careful, the word Demi-God almost implies a direct avatar or descendant/offspring of a God.
Well I don't agree at all..if it's an avatar, it's an avatar. If it's a demi-god, it's a demi-god. Those are clearly two different things.
We have a couple of characters who are specifically implied to be avatars, literally gods in mortal guise. Wulf was one, as were the handful of people you had the option of rescuing while questing for artifacts in the Imperial Cult. These were literally mortal disguises for Divines.
A demi-god, on the other hand, doesn't directly represent a god. It's often the offspring of a god, or the offspring of an offspring (et. cetera). An avatar can be destroyed, but that won't destroy the original Divine behind it obviously. Akatosh manifested as a huge golden dragon and fought Dagon, who was also an avatar. Both avatars were destroyed, but neither god is dead, obviously.
However, when Morihaus died, he was just dead. Because he wasn't necessarily immortal. He was a demi-god. A semi-divine. Umaril is the same way. There are ways to utterly destroy the offspring of a god because their blood is diluted somewhat. The farther down the line you get, the easier it is, I imagine. The great-grandchild of an Et-Ada would be nearly indistinguishable from a mere mortal, perhaps with a slightly longer lifespan and physical stamina. Obviously Umaril had extra help from Meridia because he "sold his soul for rock and roll" to gain a sort of Voldemort-esque form of immortality, which could obviously be severed regardless with a powerful enchantment.