Less of a question for this sub and probably more for an etymology sub if there is one, but the dictionary definitions serve well here:

From Dictionary.com:

a body of citizens enrolled for military service, and called out periodically for drill but serving full time only in emergencies.

Also from Dictionary.com:

a disorderly or riotous crowd of people.

Essentially, a militia is a trained and armed military organization intended for emergency use, whereas a mob is a bunch of angry people.