What's the difference between a "sweat group" and a "no-sweat group"?

ANSWER: Nothing

The Sino-Korean word 불한당 (不汗黨) means "a group of robbers or bandits," but the Chinese characters literally translate as "no (不) sweat (汗) group (黨)" or "a group that does not sweat." 한당 (汗黨) is just the abbreviated form of 불한당, so 한당 and 불한당 both mean "a group of robbers."

According to THIS KOREAN ARTICLE, the origin of the word is unclear, but there are, at least, two suggestions for its current meaning.

One suggestion is that a group of bandits are so heartless that they do not sweat over, much less cry over, the atrocities they commit. The other suggestion is that rather than work hard and "sweat" to make a living, bandits choose to steal from those who have sweated to earn what they have.