Generalizing here, but in Colorado, back country skiing refers to skiing outside the boundaries of the ski resorts. In most cases, you access the skiing by hiking in, hiking uphill, or dropping into the area from a pass. Some ski resorts may allow back country access from their area, either through gates, or at access points near the top of the lifts, or even via snowcat transport. Not all resorts allow this, in some cases you can have your pass pulled for ducking under the boundary ropes to get to the out of bounds or back country area. In CO most (not all) ski resorts operate via a user permit granted by the Forest Service because the resorts are on Federal Land.
Resort skiing can be defined by - Do I need a lift ticket?
Back Country skiing or boarding to me can be defined by - Do I need an Avalanche transponder, and avalanche rescue training? Back Country skiing is a level of magnitude more dangerous than skiing within a resort boundary, we lost the grandson of the founder of Vail resort this past weekend to an avalanche that occurred in the back country (though only a mile or so from Vail itself). Avalanches within a ski resort are still possible though much less likely, ski patrol actively manages the snow pack within the resorts, and in some cases, will even manage the snow pack in the back country by blasting snow to clear potential avalanches in popular back country areas. Some places I frequent, like Arapahoe Basin are probably 70% black or double black runs, and the areas between runs is open game. One assumes the risk that there may be obstacles, rocks or trees in these areas.
When I read the initial reports on Scheuy's accident, I incorrectly assumed this was in the back country (off-piste), and I now understand I was wrong, and that the accident occurred in the area between two marked trails (not out of bounds, not back country, but still called off-piste). In my mind, that makes it all the more shocking.
FrederikB, in the US the right of public access applies only to Federal, State, or Bureau of Land Management land, not private property (in almost all cases).