Yeah, pretty much. I think heroism in general orbits around the central idea of I believe that the world can choose to be better, and how it shows in different characters depends on where the focus lies.
For Superman that comes out as people can be good and for Batman it comes out as things can be fair.
In a lot of cases, Superman models ideal behavior. Being nigh-indestructible lets him function as basically the ultimate antidote to the bystander effect; a person who looks human (face unmasked) but can safely lead the way into adversity to help others. It’s the idea that people are fundamentally good and just need a reminder/ someone to show them how. He’s also the fantasy that someone with massive power would use that power to unconditionally do good.
Batman meanwhile, prioritises accountability. He’s the manifestation of a guilty conscience, the shadow in the night that comes for people who do bad things for selfish reasons. But he’s also fair - there’s a reason why some of his most iconic conflicts (outside of his rogues) have been him taking down mob bosses, businessmen, bankers and politicians (rather than, say, beating up poor people for shoplifting). A well-characterised Batman is one who saves the shoplifter from the corrupt mayor. It’s the idea that, for people to be good, there needs to be a fair system - one that won’t punish goodness or reward exploitation. (It’s not the reason why he wears a mask but I think there’s some good symbolism in the idea that, from the public’s perspective, the Batman could be nearly anyone.) He’s also the fantasy that, even when the privileged/ powerful/ corrupt abuse their power, justice will still come for them and their victims.
And something that’s really unusual is that this kind of flips in their civilian identities. Public figure Bruce Wayne is the mythical ethical millionaire/ billionaire; someone who uses his significant power and influence to unconditionally help Gotham and it’s people to be better. Meanwhile Clark Kent, mister nobody-special-from-Kansas, is often an investigative journalist; the little guy who helps expose the big guys who misuse their power.
This is part of why they’re such good character foils for each other. Batman may see Superman as somewhat naive and Superman may see Batman as being something of a paranoid downer, but at their cores they respect each because they share a similar central ideology and at times even methodology (just at different ends of the Sliding Scale of Superheroic Idealism Versus Cynicism).
The world can choose to be better, it just needs help. Superman is a symbol of hope for people to be better. Batman is the hope for things to be fair.