Is that really a big difference?

Huge.

The south thought of a slave as a slave. And their children would also be slaves.

The North viewed them as enslaved humans, who were just humans once they were in a state without slavery.

That is a deep and fundamental difference. It changes so much about how both sides viewed slavery. The North was ok with some escaping, but they really weren't going to lift a finger to stop it either.

While the South literally saw them as property.

If Lincoln had caved, it would have turned I to a total shit show. Not just northern cops, but "bounty hunters" who would likely grab any Black person they saw.

You really don't see why details are important? I can just let it go if it doesn't.