Difference between negatives
What's the difference between 말다 (e.g. 마십시오 or 맙시다) and 않습니다? Both are negatives. Is the difference literally that one is used in imperative/propositive and the other in declarative?
As a general rule, use 말다 to express things like, don't do that thing you always do, or don't do that thing you're doing right now.
-복도에서 뛰지 마세요 (Don't run in the hallways)
-화내지 마세요 (Don't express anger) [note: 화내다 is kind of a weird way to say being angry, it turns anger into a verb but doesn't strictly describe only outward expressions. It''s sort of directly translatable as "to generate anger"]
-야식 먹지 마 (Don't eat midnight snacks)
-결혼하지 맙시다 (Let's not marry)
않다 is less like Don't and more like Is Not, or describing a subject as someone who doesn't do a thing.
-우리 학생들은 복도에서 뛰지 않는다. (My students do not run in the hallways.) [also expressible as 우리 학생들은 복도에서 안 뛴다.]
-그는 화를 내지 않는다. (He does not express anger.) [also expressible as 그는 화를 안 낸다.]
-너는 야식을 안 먹는다. (You don't eat mindnight snacks.) [also 너는 야식을 먹지 않는다.]
-우리는 결혼을 안 한다 (We do not marry.) [also 우리는 결혼을 하지 않는다.]
So in sum: 말다 is Not Do, 않다 is Not Be
말다 implies agency so is usually applied to persons, whereas 않다 can be applied to anything I hope this makes sense
Also: 말다 must be related to 말리다 in its meaning as 'to stop someone.'
And it also comes up in some non-imperative contexts
나 어제 숙제 하다가 말았어 어떻게 하지? (I started and then stopped doing my homework yesterday what should I do?)
어제 저녁에 숙제를 하려다가 말았어. (I was going to do homework last night but then I didn't.)