The former, but the creepier part about the latter was that our fb communication was pretty limited and we never listed ourselves in a relationship.
I read on some conspiracy theory blog that corporations are tapping into the microphones on people's devices to use what they converse about to gather targeted advertising data. It all sounds like rubbish to me, but in light of your story here, maybe for once the conspiracy nuts are on to something...
If Facebook is engaging in that sort of nefarious activity, perhaps that's how they found out you two were dating.