If you have a definition you think is better, by all means propose it.
I mean, yeah? The only supernatural entity in the cosmos, worshiped by its people? Seems like a god to me.
Divinity and sacredness are defined by those who worship the entity as such, no?
But what sets that subset of divine beings apart from those that are excluded? If it’s something other than being worshipped, I don’t see it.
In D&D Gods are generally a subset of supernatural being.
They have been used in a couple different contexts throughout D&D.
First: As a source of power and sometimes a relationship for clerics (usually) and sometimes other divine magic classes (druids, paladins, rangers, etc.). In AD&D's 1e DMG they were the only beings who could grant high level clerical magic. Rituals could do first and second level spells with no god, and lesser divine beings could grant mid level cleric spells and the top ones were gated behind the demigod, lesser god, greater god hierarchy.
There was some exceptions to this with 2e philosophy clerics and 3e concept clerics not needing gods to tap divine magic.
D&D has at points gone in hard on the divine versus other power source distinctions so gods are connected to divine power and things like arcane warlock patrons are categorically different resulting in both giving power but in different categories.
Secondly: as tough monsters. They have stats or manifestations of them do and they can be fought, sometimes as an end boss. This has varied on how defined they are and what the defining characteristics. Whether they are beings with defined powers (1e Deities and Demigods) or narrative cosmological figures where specific manifestations have defined stats (2e Forgotten Realms god books) has varied.
Third: as a narrative element to justify some neat weird stuff with some thematic connotations. This god did it is similar to magic did it but can throw in distinctive flavor elements of the specific god.
Fourth: Sometimes gods are tied into worshipers. There is often a relationship between worshipers and a god's power. This has varied by sourcebook and world story.
Fifth: Gods are sometimes tied into the the afterlife of their worshipers. In lots of D&D the death cosmology ties a worshpper to their god on the outer plane once they die. There are exceptions such as 4e and the Shadowfell, Eberron and Rokugan with their different death/ghost planes.
Sixth: The planes. Sometimes godhood is defined in part in removal from the world to other planes. In some D&D only lesser gods can be on the world, with greater gods only making certain manifestations on the world and needing to primarily be on the outer planes. In 4e the astral was the general source of divine power and the home of most gods with exceptions for Torog trapped in the Underdark due to a specific story and the Raven Queen's connection to the Shadowfell as the death goddess. This has varied a lot. 2e Greyhawk mentioned the specific things of gods agreeing to stay off the prime material plane with exceptions like Cuthbert being allowed to manifest to balance out Iuz, while 1e Greyhawk had a bunch of gods whose plane was listed as the material.
Seventh: Gods can be born or made. Ascension is often a thing in D&D, though usually there are also natural gods who were always gods.
Eighth: Gods may or may not be immortal. Whether gods can be killed or whether only manifestations of them can is something that has varied.
Ninth: Hearing prayers, divine senses, and divine intervention. This varies a lot but some D&D grant gods the ability to hear prayers to them, sense things in their portfolio, and or mess around in general on the mortal plane. Sometimes this is in class features like clerical spell selection and paladin code violations where the gods directly make judgments that impact specific characters, sometimes it is like 3e deities and demigods where all gods can sense things related to their portfolio. Other times gods are statted as powerful monster/heroes with no such special thematic senses.
Tenth: Beings who are worshiped by denizens of the world or recognized as gods. Narratively this provides justification for churches, temples, cults, crusades, sacrifices, rituals, and such as elements in the game.
The definitions and dividing lines vary a lot and can be fuzzy. Throughout D&D there have been a lot of gods across a broad spectrum, but also throughout D&D most supernatural beings have not been considered gods even though they could serve a lot of the same functions as gods.
In my own campaigns I generally keep it vague like Eberron where there can be lots of theories about gods and the divine, but little that can be definitively pinned down. I like cosmologically to go with divine as a power source thing and clerics and such to simply be spellcasters who tap into divine power even though a lot of them believe it is because of specific gods directly and consciously granting them power. This also allows a range of gods as beings so Thor could be a cosmological storm god, a being with tons of divine power and a storm aspect, or a being who hits giants hard with a hammer, or an actual D&D storm giant, or not exist at all. I like the idea of cults to gods that do not exist, or to hero worship like the Greeks had, or ancestor worship, or non deity religions, or to worshiping powerful but non divine beings like giants and dragons who get no extra power from it at all. I also like having divine beings like angels and varying gods. I think the idea of gods as Mage the Ascension style paradigm workers but inverted in part to be shaped by worshipers conception of them is a fun one.
