When I first proposed the idea of a cleric whose divine powers came from being a demigod — a half-deity — one of my good friends, also a long-time gamer, took exception with the idea, contending that a demigod character with entry-level (first-level) abilities might be fine for a novel, or for fiction, but that that is not how demigods in D&D work. He has a point, in that 3rd-edition bestowed the label of demigod on beings that had divine ranks of 1 to 5, and that any 5th-edition character with abilities on par with 3rd-edition’s divine ranks 1 to 5 would be grossly overpowered.
However, I disagree with my friend. There is a difference between the term demigod used to mean “child of a mortal and a god” and the term demigod used to mean “divine ranks 1 to 5 in 3rd edition of D&D.” The first usage is the more historic, more established usage, and is simply a statement of lineage. The second is a bit of 3rd-edition bookkeeping designed to keep stat blocks clear.