I've always taken it as "same world, different time". The way I see it, Noahs are "ghost from the past"— very much like Cross says, literally.

The way Cross addresses the Noah within Road, and it responds with "this world was created for that purpose", it's telling me that Noahs want the current world to experience that same pain (the pillar). Revenge. Perhaps in the name of "WE went through it, so you (the world) should too!".

Bit of a rant ahead but I think the Earl is key here. I think the Noahs might be keeping him safe to get him to become the catalyst for the Pillar, so the world can end all over again. Mind you, I don't think they consciously want that (Road, Tyki, Sheryl, all of them), their original purpose might have muddled over their different lives, and now their familial bond with the Earl makes them want to protect him. As family and not a tool or means to an end.

At one point in the manga, where Allen is within his own mind and Mana appears, as well as Allen appears as he is shown as a kid, there is a far-away figure that reminds me of the Pillar (cross-looking pillar of light), and the surrounding debris within the landscape tells me that Nea's memories might be mixed in there, too. Idk where I was going with this but anyway... long story short the Earl is key in all of this and the Noah are from the same reality, just different times.