I think you've hit the nail right on the head with this post!
I suppose this is where the concept of the 'Real Clark' comes in. Or, another way of putting it is the distinction between 'Smallville Clark' and 'Metropolis Clark'.
The part in your post that I've highlighted in bold though...well, I suppose that question can be answered differently in different eras.
If you consider the original Golden Age version, we actually don't know much about his formative years. Based on what we know though, I'd argue that he's the 'Real Clark'. He grew up thinking of himself as Clark Kent, and no one and nothing else. He didn't even know about the rocket! His parents taught him to use his powers to help people. After their deaths, he decided to use his powers to become the costumed hero known as Superman. And he disguises himself with a pair of glasses and poses as the mild-mannered reporter Clark Kent for his civilian identity. As Clark, he's forced to act like a weakling, but as Superman, he can be his 'true self'. But fundamentally, he thinks of himself as Clark Kent because that's all he's known...until, years later, he learns about his Kryptonian heritage.
But with the Silver Age/Bronze Age version, it gets complicated. This version apparently knew right from when he was a young child that he's Kal-El from the planet Krypton, and he identifies himself as such. But he's also raised with the identity of 'Clark Kent', that he knows isn't the name he was born with. And he reveals himself to the world as Superboy as a pre-teen, being able to freely use his powers, while hiding his identity and blending in with the other kids as the bespectacled Clark Kent. So does this mean that 'Clark Kent' is a construct from Day 1, given that Kal-El always knew who he really is and that his life as 'Clark' was an illusion?
Byrne took us back to the Golden Age by having him grow up believing himself to be Clark Kent. Here the twist was that, glasses notwithstanding, he pretty much acts as his 'true self' when he's acting as a reporter in Metropolis i.e. there is just one Clark Kent who's the 'Real Clark'. Superman is the illusion - the false identity constructed so that Clark can use his powers freely in public. He later learns that he is Kal-El from Krypton, but isn't really enthusiastic about adopting that identity, continuing to consider himself Clark Kent first and foremost.
I think most versions ultimately give us a 'Real Clark' that he grows up as. The differences crop up mainly with two factors - 1. How much of an act does he put on when it comes to playing 'Reporter Clark'? And 2. How much does the knowledge of his Kryptonian heritage and identity as Kal-El affect how he thinks of himself?
The Silver Age/Bronze Age though is an outlier since it suggests that Clark Kent was a construct from Day 1 since he always knew he's Kal-El!