the definition of alpine climbing

When I climbed my first routes in Canada such as the north face of Chinamans (sorry, Ha Ling now) or Yamnuska I called it alpine climbing. Cliffs like that in Europe were considered as alpine climbing, simply because it was happening in the alpine (above tree line more or less). Now here in Canada I've been told that this is not alpine climbing, maybe alpine rock climbing at best. Not that I want to argue with this, but nobody to this date was really able to tell me what ingredients are needed to call an outing alpine climbing. Although I heard comments like: there has to be ice somewhere on the route, like the picture above, or you have to suffer a cold bivy (or suffer more with spending a night in a snow cave with a chain smoker like me).If you look in the canadian alpine bible-Selected alpine climbs in the Rockies-there is a wide variety of climbs, a lot of them resemble what Chinamans or Yamnuska has to offer. What is the difference between Brewers Buttress on Castle versus Direttissima on Yam? Or a Gmoser Route on Louis or the East face of Mt. Bable, the list goes on and on. Anyways, if someone could help me out in describing alpine climbing to me in a few sentences, it would be much appreciated. Whoever comes up with the best description which makes the most sense, I will by as much beer as he/she can drink in one evening in a local pup of your choice.