Manhattan Exclusion zone, aka New York Raid, aka NYR is a dungeon in New York with 4 difficulty modes (story – Elite 1 – Elite 5 – Elite 10) and in weekly missions the story counts along with one of the Elite modes. You can complete it as many times and you want, but the rewards really worth it only the first time. You can spend time better instead of running the dungeon multiple times and it resets every Tuesday.
Pug is a “Pick Up Group” meaning that random agents either in group matching or some other way get together from multiple cabals to complete the task. Story is easiest and Elite 10 hardest with a lot of differences in between.