I count any being, group, or concept, that has the power to grant spell use as some sort of divinity - even if it grants arcane spells. So technically this includes gods and goddesses (of any ability), devils, demons, mysteries, patrons, philosophies and anything else that can grant spells. Just as importantly, Priests don’t need to know that they are priests, conduct rituals or services - they just need to act as an example of the behaviour the power wants to promote.

I think that (just about) covers everything. If it doesn’t - just pretend that it does :P

• Primordial Power: This is almost a back definition, based on the descriptions below. Primordial powers are the very stuff of the cosmos – the essence of life, death, magic, nature, pain, anger, law, art, music, chaos … All mortal life rolled into one. It was Primordial Powers that formed our Prime Material and underpin it. It was Primordial Powers that allowed mortals to survive the God Wars, and Primordial Powers that kickstarted both the first and second generation of gods. While they are the very essence of everything, they are completely inaccessible to mortals. However, some sages believe that all of the lesser powers, Deities, Demi-gods, Quasi-deities and minor powers -get their abilities (including their divinity) directly from these Primordial Powers. They are the driving source of everything.
• Deity: The standard Paizo definition is <i>any divinity that doesn't get a stat block</i> – although there have been a few ‘extra elements’ thrown in occasionally along the way. One definition element I liked is that they are ‘incomprehensible’ to Mortals. In other words, mortals know they exist, but don’t really understand them, nor can they second guess them. This means that a full deity can have more than one church, with different philosophical interpretations of the faith – for Example: in my game world Wee Jas has three different churches - with three different interpretations of how her faith should be represented.
• Demigod: The standard Paizo definition is <i>any divinity that gets a stat block and is almost always level 26–30 and is thus generally out of reach of typical groups.</i> Demi-gods are much more ‘comprehensible’ to mortals, and are (in many ways) more predictable, relatable and personal than full deities – their churches tend to share a philosophical interpretation of the faith.. There are many more demi-gods than deities, and many demi-gods operate as assistants or subsidiaries to full deities. Paizo lists many types of demi-god https://pathfinderwiki.com/wiki/Demigod
• Quasi-Deity: In the past there have used terms such as Hierophant, Godling, Quasi-Deity, Hero God and Nascent Power to imply an immortal able to grant spells but with less power than a Demi-god. However, the current pathfinder definition is <i> any divinity of level 25 or lower with a stat block and is thus in the reach of typical groups.</i> Paizo lists malebranche and nascent demon lords as examples of quasi deities, and there are probably others scattered around.. I am going to add powerful Mythic NPCs who can grant sixth level spells to their priests. To further differentiate Quasi-Deities from Demi-gods and true deities, I am going to restrict them to granting spells from the Adept spell list. Like demi-gods, many (probably most) quasi-deities are assistants, subsidiaries or even servants, to higher ranking deities.
• Minor Powers: This covers everything else that doesn’t quite fit in the ‘Standard Mortal’ category. For example: Immortals without the ability to grant spells to followers; most mythic characters; any Divine Source that cannot grant 6th level spells; Nature Spirits. Basically, any entity that might gain the ability to grant spells or might, somehow, ‘come to the notice’ of The Cosmos itself.

More interesting, is the question of how mortals become deities - at the moment I am aware of a number of ways.

  Gift of the Gods - there are all sorts of stories where a mortal (or some other creature) has been raised to a deity by another god. For Example, 'Nivi Rhombodazzle traded a special gem to Torag in exchange for becoming a demigoddess'and of my homebrew deities, at least two (Takri and Arth) were gifted their deific status by other deities. There are similar stories in just about every other rules set. That just tells us that many deities have more Shards of Divinity than they actually need, or can gather them very quickly, to be able to bestow them on another.
  Inheritance - sometimes a god dies and passes their divinity and/or portfolio to another, for example Midnight became Mystara, in the 3.5 universe. However, it might be that a deity is killed in a fight, and the portfolio is 'stolen' by the victor. That could be another deity, feeding on the death or a peer, or a particularly powerful mortal (devil, demon etc) taking on a weakened deity and stealing their powers. Often times there will be a few shards of divinity left over, that just get lost in the ether …
  The Starstone - Pathfinder has the Starstone as a shortcut to deity. You jump across to it, face various trials and, if you succeed, become a deity of some sort. Cayden Cailean, The Lucky Drunk, is probably the most well known of these.
  Mythic Deeds - as PF Mythic characters progress, they can gain mythic levels by becoming involved in events of cosmic / mythological importance. In my system, that just means they are in a position to absorb a stray Shard of Divinity. Each 'Trial' gains them one shard of Divinity - unless the DM decides differently. A character needs something like thirty trials/shards before they are a real power. However, by choosing the right abilities, they can become a quasi-deity after four trials (when they become tier 3) However, the spells that they can grant are very limited. I tend to restrict quasi-deities to Adept spells - just to add a bit of differentiation. I miss the days when Demi-gods could only grant 5th level spells, etc …