Even if you handwave that the ship is different (though a set of stairs on the bridge do not a new class make), how do we explain the same people being in the same positions on the same ship?
Except it wasn't the exact same people, now was it? Troi and Worf were absent, while Yar was still alive. Only the rest of the command staff remain, however, we don't know how many of the "no name" crew members remain. For all we know, most of the crew is different.