Would you mind +ving vs other requests...

[m21vp]

Sometimes I have problems with the two versions of these requests. Both are requests but can be confusing as one of them the answer is yes, but the other, the answer is "no".

Eg. Would you mind closing the door? No.
Could you close the door? Yes.
Would you stop smoking as the smell makes me sick? Yes

How could yo explain easily would you mind vs other requests?

[Bennevis]

Would you mind closing the door?
=
Do have any objection to closing the door?
No, I don't.