NCT is the the big group. NCT127 is a fixed unit based in Seoul, NCT U has a flexible lineup, NCT Dream is the kids with a graduation concept.
Edit: To be clearer, NCT127 has 9 fixed members.
NCT U were 5 (Seventh Sense), then 3 (Without You), then another 3 (Without You Chinese Ver.), then the original 3 (Timeless) then now 7 (BOSS).
NCT Dream had Jaemin on hiatus but he's back, but Mark will probably graduate soon.