I can’t understand the difference in meaning and nuance between
“Stop whining about it!”
and
“Don’t whine about it!”

Could you please explain it to me?

See a translation

“Stop whining about it!” implies that the listener has been complaining for quite a while. For example, if I have been complaining about the cold weather to my friend for at least a minute, she could tell me “stop whining about it!” if she is sick of hearing me complain.

“Don’t whine about it!” could be applicable when the listener just started complaining; the listener has not been complaining for a long time. It is also applicable when the the listener has not actually complained, but the speaker assumes that he will (so he uses this phrase with the mistaken assumption that the listener is going to start complaining at some point).

Both sentences tell the listener to not complain, but (to me at least) the difference lies in how long the speaker has been hearing the listener’s complaints.