There are two high-level membership types, Current Members and Past Members. 

Current members are active members of your group. Past members are members whose membership end date has expired. 

Those under Contacts are non-paying individuals who may have signed up
for events you sponsored or those you have added in as contacts for networking purposes.

Essentially, a contact will have a very restricted access compared to a member (no access to the group page of a group, will not be targeted in emails only sent to members if the contacts are not selected when composing an email, excluded from event registration access or specific event tickets if the event is set up to only allow members to register...).