I can empathize...

The difference, if any, between a marriage not enforced by the state/church - or in a country/past era/etc etc where the state/church did not get involved, and a couple simply shacking up together?

I think in the past there was a social contract even if there wasn't a civil contract.  In other words, the couple announced that they were getting married and committing to each other and there was some ceremony sanctifying the marriage by the community.  Violations of the marriage were handled by social pressure.