I've been a little bit confused when people report their site visitors. Some say they have N visits per day, other may be more accurate and say N views/page loads per day. Some speak about uniques. So, when someone claims to have N visits a day, what is actually being said? To me it seems -- and correct me if I'm wrong -- that is can mean either of the two things: That a page in their web site is requested N times a day, that is, there have been N page loads. That N different (to the extent that it can be known in the web) visitors have visited their site, that is, uniques. These are two very different things, to me at least. One could easily have 100*N page loads but only N different visitors. So I would assume that people were a little bit more accurate what they really mean. Especially, in the context of AdSense.
You are basically right. There should be a standard accepted measure, and most people do cite unique visitors, as it's the truest indication of your site's performance