Muggy is technically a slang term that is often used to refer to weather that is hot and humid. Muggy is humid but humid isn't necessarily muggy. If you think of the example of cool fog, i.e., fog containing a high amount of water or water vapor; it is noticeably moist, humid air, but not hot. In day-to-day English "muggy" is a common word for hot and humid.

I am not a native speaker, but I guess humid means warm and dam in a pleasant way, while muggy means in a unpleasant way .

It's basically the same thing. Muggy = Humid Though when its humid it can also be cold and wet, which equals to foggy.

To me, the meaning is same. The only difference may be that "humid" sounds lightly more formal.