The Galaxy-class USS Yamato is numbered NCC-1305-E. Perhaps the original NCC-1305 was one of those badass Newton-class ships, and it died a heroic death some time prior to The Original Series.
Earth always looked the way it does in Star Trek and Star Trek Into Darkness, we just never saw it in it's glory until now (actually, that's the truth I think...?)
The way things look in Trek is fluid. If you can recast an actor, you can update or swap out the look of something just as easily. Maybe TOS "really" looked a little more like THIS