What in fact is Sunsoft and Genesis?
Genesis: a Sega console. The Genesis version of Lemmings has around 100 [EDIT: not 80] extra levels not found in the Amiga version.
Sunsoft: (1) The company that made the Genesis version;
(2) The last difficulty category in the Genesis version, mostly equivalent to Taxing difficulty, with some very hard levels towards the end;
(3) The last difficulty category in the SNES version, containing just five extra levels specially selected from the Genesis version;
(4) In descriptions of CustLemm and Cheapo levels, often used, with reference to (3), to mean a difficulty ranking higher than Mayhem.