The confusion, I think, comes from the conflation of two separate questions:
1. In ski area boundaries our outside (in-bounds, or "backcountry")
2. Downhill skiing, Randonee/Touring, or x-country (nothing to do with backcountry since you can do all of the above in bounds or in the backcountry).
Backcountry, at least where I grew up in the PNW in the 90s, only pertained to where you were skiing, not to equipment or technique used to ski it.
