Maus, I’m sure someone like Fenris will be along with a more definitive answer than this… but as far as I can tell, Captain Marvel and Billy Batson share the same mind in different bodies. Captain Marvel IS Billy Batson… Captain Marvel is a real adult they way that Tom Hanks was a bonafide adult in the movie “Big”. They share experiences and memories in a very vague and ill-defined way.
Miracleman, on the other hand, shares existential space with Mike Moran. They are two very different personalities that grew from the same mind, and share memories and experiences that are vastly shaped by their experiences and perceptions. When Mike Moran changes to Miracleman, they trade two minds tethered to bodies that swap places in real time: the other mind/body is stored in a vast warehouse of bodies held in in stasis in underspace, while the mind/body in real space/time grows, ages and dies.
Though I think Fenris would agree that while Billy is intellectually mature as Captain Marvel he remains as socially immature as he is in the form of Billy Batson.
While DC has aged Billy a bit and recently had him in a romance with Star Girl, when Beautia hit on him he didn’t know what to do. He was quick to jump to conclusions about Black Adam and was in the JSA to watch him.
His world is very black and white. Partly created by his youth and partially created by the power he has as Captain Marvel which makes his mind very clear and focused.
There have been numerous instances where the Billy and the Captain (have you ever been to sea?) referred to each other in the third person: “Gee, I’d better get back to the station before Billy gets in trouble! SHAZAM!”
I’m pretty sure the deep psychological issues were not considered when the character was created. It was more marketing than anything else; describing a boy roughly the same age as the ones who typically buy comics, conveniently orphaned, who essentially can become Superman by saying a magic word.
Well, the original Fawcett Captain Marvel was just a big Billy Batson. Not more mature (though he was probably smarter). He was a big kid fighting crime completely deadpan.
I gave up on CM once they darkknighted him. The original was just plain terrific; now that they made him a superhero like problems – like every other superhero in comics – he’s not worth thinking about.