Truthfully, I consider it not the same guy going only if I go by the fact that I can clearly and immediately tell the difference in which Superman I'm supposed to be reading. However, I feel as though the four main Supermen all absolutely connect with each other. To me this is what prevents Rebirth Superman from "only" feeling like one era. It's never been a case where I couldn't feel one of the other three in the adventures of one, even if the continuity was very different.
When I think of "different" I think of say, Lana and Kristin Wells.