Gollux

It's the difficulty you beat him at, yes. It affects the drops you get.

Clear 1 = Easy mode
Clear 2 = Normal mode
Clear 3 = Hard mode
Clear 4 = Hell mode when you leave the map even once
Clear 5 = Hell mode when you stay in the boss map for the duration of the fight

clear 4 is a bit wrong I finally understand ....

they both hell mode

Clear 4 = 1 Player (Solo) It doesn't matter if you leave the map or not
Clear 5 = 2 or more player (It doesn't matter if you leave the map or not and whoever leave the map first or not it will always be like this
(The first player who enter the map will always shown clear 4 and when the rest of the player enter it will say clear 5 for them for the first player will say both instead just one )