Not much, at least not for the purposes of this discussion.
To someone who actually knows the difference between a carrier and a battleship, saying there's not much of difference between the two is like saying there's no significant difference between a tank and an airplane.
I think we all know the difference, but old BSG didn't hold to that distinction itself: Pegasus
went in to fight the Cylon base-ships on her own, something a r/w carrier would never do. Also, the "fighters" never seemed to have much of a ship-killing role on their own, they just fought each other. The battlestars ended up looking more like a carrier-battleship hybrid than anything else.