In reply to Shannon_G123:
You're probably seeing alpine climbing, alpine style, expedition, expedition-style, and mountaineering. They're all mountain climbing, but there are distinctions.
Alpine climbing - ascending high mountains by long routes, often glaciated and often involving snow and ice climbing, but in some cases can be all rock climbing. Usually done on mid-height mountain ranges (ie. the Alps), summits 3000-5000m, where most routes can be done in a day (unless they're extremely difficult). The guide to this kind of thing is usually a surly little Swiss man, or a Kiwi who is usually named Russell, or Murray.
Expedition - usually a group going to achieve a particular objective, usually exploratory or adventurous in this context, not a guided tour to a low or popular objective (ie. climbing to the summit of Kilimanjaro is not really an expedition, climbing Mont Blanc is not an expedition, but a four-week trek across multiple 5000m+ passes through seldom visited Himalayan ranges, even without summits, could reliably be considered an expedition. Climbing K2 in any way will always be an expedition). The guide to this kind of thing is to get enough experience on your own of the activity so you can tell how much of the brochure is bullshit. Expedition is a sexier and more intrepid name for 'trip', so most of it is bullshit.
Expedition Style - refers to the way an expedition group climbs a mountain, usually shutting back and forth along fixed ropes to supply multiple camps, using porters above base camp etc. Considered to be old-fashioned (1930-1970) in traditional climbing terms, but since the 1990s has been the style in which nearly all commercial guided Himalayan expeditions are done because it's the only way to get incompetent rich people to 8000m summits. And sometimes down again. The guide to this kind of thing is 'The Ascent of Rum Doodle' by WE Bowman.
Alpine Style - as opposed to Expedition Style, this refers to just starting at the bottom and climbing to the top, no back and forth shuttling, no fixed ropes, no use of porters above base camp. You can stop and camp/bivi, maybe for a day or three, but you keep going up. A superior variation on this is Single Push climbing, where you go bottom to top but don't bivi or camp, just climb continuously with short breaks, for maybe 10-60hrs. Though there are pedantic factors to alpine-style (not being on the route at all before climbing it etc) there is no such thing as 'alpine style from Camp 2' having climbed the lower mountain in Expedition Style, for example. The guide to this kind of thing is The Shining Mountain by Joe Tasker and Peter Boardman, if you have a beard, or something that mentions Votyek Kurtyka and a cast of very small but fit Frenchmen.
So, you can go on an expedition and climb the mountain Expedition Style.
And you can go on an expedition and climb the mountain Alpine Style.