Looks like Jr. is getting confused again, there is a difference between mountaineering and alpine climbing.
Mountaineering is generally the easiest and safest route up an objective. (Example: the DC route up Mt. Rainier. Generally long snow slogs, crevasse travel and easy angled snow/Ice) It is uncommon to have lots of Ice and belay stations involved.
Alpine climbing is much different. That would include the shortest and or most difficult route to your objective done in a fast amount of time. (Example would be a route with multiple pitches including rock/ice/ and or mixed climbing and maybe even aid, maybe a night or two, lots of exposure and use of a lot of technical gear.)
The brevity of my definition limits me to more detail, but if you want more read Freedom of the Hills. I think you would learn a lot.
And to answer your question, yes they are both dangerous in their own ways.
"Hey, careful, man, there's a beverage here!"
- The Dude, Lebowski