"If the South had won, we wouldn't be The United States, we'd be two different nations."
In the event that a draw was fought and the north accepted
the succession yes.
But not necessarily, had the south "won",that is had they vanquished the north, there might have evolved a Unified States of America, and it's certainly possible that while
it would have been different to begin with, after a hundred
and fifty years, it might look much as we do today.
Indeed it might. It also might not.
Southerners wouldn't agree to reunification unless it provided strong guarantees to their institutions -- very much including slavery or segregation. There'd be a demand that the federal government could never pass something like the Civil Rights acts of the 1960s. That in itself would have made any reunited country very different from today's America.
Northerners wouldn't agree to Southerners' demands, and there'd be a desire to wash their hands entirely of the region. Since the compromises of 1787 and 1820 and 1850 hadn't been enough for the South, Northerners might not go down that road again. We would have been a more inward looking country, or pair of countries, and far less of a match for the rest of the world.
It's certainly true that the parts of the US and the countries of the world have been growing closer together over the last fifty years or so. That's someting to take into account. But it's not as though history was bound to end up more or less where we are now. Had events taken a different turn in the past, the world of 2006 might have ended looking very different than it does to us.