Hi Richard,
I didn't see your questions answered yet (maybe I missed it, I just skimmed) Yes, essentially Alpine is downhill skiing, and cross country is just that. Technically, it is different equipment and different skiing styles, but as far as what they are, there you go.
In the context of this thread, I believe this is what you are looking for:
Tyrolean Traverse
To save you from going there, in a nutshell this is a method of using ropes to traverse steep pitches.
In other news for the ski patrollers here, I passed my senior EMM 2 weeks ago. My patrol director peer pressured me into doing it. I'm not one for titles and that seems to be all "senior" is really good for. Nonetheless I passed and I thought the exam was relatively simple, so if you're considering it, go for it Perhaps next year I will try the ski and tobaggon portion, but with grad. school and a 17 month old at home, I couldn't do it this year.
Hope all is well to the 'HH'es. When is your mountain projected to close for the season? We should make it to our projected date of 4/20. Not bad for a southern NYS mountain, eh?
-skibum