It's going to take me a little while to process this but I do have this to write. It seems as if everyone is saying Rose wasn't our Rose but I beg to differ. Given she had the whole of The Time Vortex within her and that she scattered clues for her self through out time and space it's not all that unlikely that she would have appeared to The War Doctor.
Time vortex or no time vortex, the Moment Interface smiling makes it feel that there is more to it than a sentient Moment being happy, plus some of her remarks are quite uncharacteristic for a Doomsday machine, sentient or not. Besides, she's credited as Rose.
Or they could be the same thing. The Time Lords never figured how the Moment got its sentience, did they? Perhaps now we know.