Just adding to the chorus here, but yes, it is incredibly unlikely that you were on an "AD" ticket. They are all space available, meaning standby, you'd have to conform to a dress code, and a lot of other rules. They're also not interline, so you couldn't do on one AD ticket an AAD fare on both BA and AA operated flights.

I bet you had a corporate agreement fare, which most likely does earn tier points (most do but yours might not).

(Incidentally, I've found that AD fares for the most part are more expensive than a confirmed/published fare, so they're not worth it.)