Well, I think if we were both sitting in a 1L class discussing this, intent would be the primary driver. In the P2P scenario, the intent of the parties is a business transaction, while in the relationship scenario, the intent is, well, a relationship - something more than immediate satisfaction of needs.
Of course, there is the time-honored tradition of 'marrying up' and 'marraiges of convenience,' but both of those are socially frowned upon (and illegal in certain circumstances).
It's as you say - not clearly black and white. But, if all parties are being honest, there are clear differences. My SO has benefits that I can't get in a P2P relationship. For example, someone with whom I can discuss intimate issues, who has a stake in the outcome (ie., if I want to quit my $250K/yr job, my ATF will never care as much as my SO, because my SO has a much more significant stake in the outcome). As much as my ATF might care about me, that one detail is not, and will likely never be, a part of our relationship. In that regard, the best the ATF can hope for is BFF status.