What is the difference between rude and mean?

Rude/rudeness (impudence) is not having or showing concern or respect for the rights and feelings of other people: not polite. Being crude, or a display of disrespect by not complying with the social norms or etiquette.

Mean/meanness is the condition or quality, of being mean; want of Excellence; poorness; lowness; baseness; sordidness; stinginess. A spiteful or malicious act.