Covox levels are the 8 levels from the demo disk
Save the Lemmings a.k.a. Covox Lemmings.
The NES levels are probably what appeared exclusively on NES Lemmings 1.
Reason: DOS and Amiga Lemmings 1 level are special in how DOS/Amiga were the first platforms for which DMA created Lemmings levels, therefore we think of DOS/Amiga levels simply as Lemmings 1 levels. Other hardware platforms (such as NES) often weren't able to run the large DOS/Amiga levels accurately, and got replacement levels. Colloquially, we call a level a NES level if it appeared on NES, but not DOS/Amiga.
Genesis got a particularly strong set of replacement/addon levels with some excellent puzzles. The Genesis levels are mixed with DOS/Amiga levels into Lemmings Redux, the level pack that ships directly with NeoLemmix.
-- Simon