Those are separate from faction reputations but they are factored into the reaction roll when you talk to any given NPC. For example, if you talk to a commoner then their reputation will initially be set to their faction's reputation and then will be adjusted by the amount of the commoner reputation.And what about the "Reputation with Commoners, Scholars,... , Underworld", how does it affect the game?
Social group reps aren't used when determining whether a player can join a guild, so that won't keep you out of one.