Difference being a valid common-law marriage is just as married in the eyes of the state as a licensed marriage. 'Concubine' clearly denotes some kind of not-quite-the-same status (the details of which have been hashed out above).
True, I use common-law marriage as an illustration to demystify concubinage. So the marriage license is like unto the marriage contract which separated concubinage from marriage for the near eastern Semitic cultures. But non-papered marriage isn't some big moral deal. They're not required today to legally have a marriage like relationship (only to have it recognized by the state) and have only existed a 150 years or so. Before marriage licensing we (the English legal tradition of the last 1000 years) only ever had common law marriage.