I noticed that the current WR has weapons that is unlocked later in the game. I personally think that would be considered NG+ (since you have the weapons in the beginning of the run). Any% would be started out with a clean file, restarting the story mode using the 'New Story' option. Timing would be the same. NG+ would have all of the weapons, and can use the 'Rewind Story' option in the mission select screen.

Anyways thanks for reading this!