Randonneuring: Randonneuring is long-distance unsupported endurance cycling. This style of riding is non-competitive in nature, and self-sufficiency is paramount. When riders participate in randonneuring events, they are part of a long tradition that goes back to the beginning of the sport of cycling in France and Italy. Friendly camaraderie, not competition, is the hallmark of randonneuring. (from RUSA.org)
Randonnée skiing: The terms “backcountry skiing,” “Randonnée,” “ski touring,” and “off-piste skiing” are often used interchangeably; (from 2009 Wikipedia.org).
In the U.S. the common term for rando skiing is simply “AT” which stands for alpine touring — hence the terms “AT skiing, AT boots or AT skis.” Alpine touring is based a style of skiing that enables one to ski uphill in touring mode with a free heel and then lock the heel down for the descent, like a traditional lift served or alpine skier. Telemark or “tele” skiing is similar to randoonnée skiing except for one significant equipment difference: tele skiers ski downhill with their heel free and with the toe portion of their boot attached to the ski.
Additionally, the terms “ski mo” (most commonly referring to ski mountaineering racing) or “rando racing” are gaining in popularity.