What is the difference between muggy and humid?

They are the same except muggy is colloquial.

http://weather.about.com/od/m/g/muggy.htm

There is none, "humid" is the more scientific term while "muggy" is more colloqiual.

"Muggy is a slang term used to describe weather that is hot and humid."

http://weather.about.com/od/m/g/muggy.htm

While muggy is humid, humid is not necessarily muggy, in that conditions can also be cool and humid, e.g. fog.

"hu·mid? ?/?hyum?d or, often, ?yu-/ [hyoo-mid or, often, yoo-] adjective
containing a high amount of water or water vapor; noticeably moist: humid air; a humid climate."
- http://dictionary.reference.com/browse/humid?s=t

"mug·gy? ?/?m?gi/ Show Spelled[muhg-ee] Show IPA
adjective, mug·gi·er, mug·gi·est.
(of the atmosphere, weather, etc.) oppressively humid; damp and close." - http://dictionary.reference.com/browse/muggy?s=t

"fog1 ? ?/f?g, f?g/ Show Spelled [fog, fawg] Show IPA noun, verb, fogged, fog·ging.
noun
1. a cloudlike mass or layer of minute water droplets or ice crystals near the surface of the earth, appreciably reducing visibility." - http://dictionary.reference.com/browse/fog?s=t