We have the older spellcaster, the psion, who's been in this game since before I was born...
Ok, so that explains a lot. So, the psion technically didn't exist until 2001 when it was introduced by 3e's "Psionics Handbook". By that time I was 28 and had been playing D&D for about 20 years. The predecessor to the psion was the "psionicist" which was in 2e "The Complete Psionicist Handbook" which came out in 1991, at which time I was 18. It was in my impression very poorly received. Feel free to read the reviews of GMs that tried to use the book.
While there was some cleaning up of the rules compared to 1e, the rules were highly unbalanced and I don't think anyone much used them unless they got big into Dark Sun which had it's own setting and unique magic system and reasons for wanting to have psionics (and it's own super crazy "it's not broken if everything is broken" take on balance). But Dark Sun also kept 1e's "wild talents" system on top of acknowledging the psionicist as an option. It did clarify the "Psionics–Magic Transparency" as official to the setting, which made psionics magic and using it spellcasting in practice, since "dispel magic" affected psionic disciplines, "detect psionics" detected magic, and so forth. So I mean, it was definitely trying to move things in the right direction.
In any event, in both 2e and 3e, the psion/psionicist was not part of the core rules and was presented in an optional guide. Indeed, 3e divorced psionics from its core rules entirely, which 2e never completely did - the 2e "The Complete Psionicist Handbook" declared itself (as one of its many internal contradictions) entirely optional even though the 2e Montrous Compendium still referenced it.
Prior to 1991, say you are going back to 1978, psionics weren't a class you could study or learn. They were magic you were either born with or else you weren't. They represented innate inborn natural magical ability that wasn't tied to study or dependent on an external force. The psion/psionicist didn't exist in 1978 at all. It defeated the purpose and intent of psionics to have it just be another class and level based thing.
And, yeah, y'know what? Wizards should lose a lot of spells. They should get an identity that isn't just "Grab bag of spells in the game"
This is to me a completely different question and one I don't have a lot of interest in. As I've said before, I am open to splitting up spellcasters in different ways to limit their power, and exactly how you split them up isn't that important to me. Personally, I'd never split them into "Psion" for a variety of reasons, but if you went that way it wouldn't be wrong. What I would think is wrong though would be having multiple different magic systems. One thing about the Cleric and the Wizard (and the sorcerer and the druid and the paladin and the ranger and whatever) that you overlook is that they share the same magic system. So if you really want to have a Psion sharing the magic system of the other spellcasting then that's fine with me. I don't like it and I would go at this in a different way with just 4 core full-casters, but you could justify it if for example you were making Dark Sun the core setting of the game.
Like I said, if you are designing a new D&D edition you should probably end up with 10-15 classes as the end of the day, and I'm not going to fight over which ones they are that much except in a few specific cases where I think there is a reason the choice is wrong (such as adding psionics purely to add another spellcasting system given the long history of that being a bad idea). But I think you'll find that this agreement about the psion, that it is magic and it's a spellcasting class using the same base mechanics as other spellcasting classes is not one which will make the people who want a psion happy.
Extrapolating this, all magic being the same, implies that divine magic is just the same again.
I mean it definitely is. I just explained that it is. So what?