A mob is a group of people caught up in excitement, most often negative. They are easily led & will do actions they would most often not do if they were alone, like hurting people or objects. They might be upper-class, if they go to a fancy university, so they are not necessarily rabble.
People are considered rabble if they are lower-class people, like on the Statue of Liberty: "Your huddled masses." These are not necessarily acting as a group, but are just present in the situation. An upper class person may label them the "rabble."