Maxperson
Morkus from Orkus
Broadly, yes. The divine ranks are talking about deities(gods) of various ranks. Demigods are the lowest rank and could rise from demigod to true god, but are still the lowest rank of "god."Are you saying DMG demigod quasi-deities are gods? It describes them as divine origin beings who in theory are able to ascend to godhood if they amass enough worshipers.
"Quasi-deities have a divine origin, but they don't hear or answer prayers, grant spells to clerics, or control aspects of mortal life. They are still immensely powerful beings, and in theory they could ascend to godhood if they amassed enough worshipers. Quasi-deities fall into three subcategories: demigods, titans, and vestiges."
The opening paragraph talks about the divine ranks and how gods can vary, depending on the plane. The ranks are not greater and lesser god, but rather greater and lesser deity. Quasideity is the lowest rank, demigods are part of that. Again, they didn't do well with descriptions here. Had the above ranks been lesser god and greater god, then it would be clear that quasi-deities were not gods. But since all three are deities, otherwise known as gods, they are all just categories of the same. In the context used, "godhood" just means ability to grant spells.