At least one reason it's called KARMA is because of specific flavor text that appears when you have enough KARMA damage racked up. The flavor texts are as follows:
You felt your sins crawling on your back. (0-10 KARMA damage)
You felt your sins weighing on your neck. (10-20 KARMA damage)
KARMA coursing through your veins. (20-30 KARMA damage)
Doomed to death of KARMA! (30-40 KARMA damage, according to wiki, but no longer used in-game because of programming errors)
As you can see, KARMA is actually named in-game, which is where part of it stems from. Now, as to where people get the 'Sans can only use this against people who sinned' thing from, I don't know. I personally don't think KARMA really means the same karma people speak of (that whole impersonal force which comes back to bite you in the butt when you screw up), since LOVE and EXP are acronyms who don't mean what we originally think either. The fact it's used in all caps makes me think it's some sort of acronym... maybe something to do with killing, since both words starts with a 'k'. However, it seems no one knows what it really means, or if someone does, I've never heard of it.
The only thing I can think of is the 'sins crawling up your back' thing, which yeah, makes it sound like KARMA is the same thing as karma. Maybe it's possible Sans can actually only use this on people who have sinned, but to my knowledge, that hasn't been confirmed.