From a life long BBQ restaurant owner:
The term "Danish Rib" refers to a baby back rib, which supposedly was the country of origin of the cut. Generally the "Danish" cut removes all the meat from above the bones, where most "American Style" ribs leave a small amount of this loin meat on the rack, providing more meat per rack. "Danish" ribs are imported from Denmark (surprise, surprise) if they are truly Danish Ribs. Denmark imports almost half of the ribs sold in America, until recently because of a ban on European Swine, due to Hoof in Mouth disease. If you ever at at a "Houston's" restaurant, you almost certainly ate Danish ribs. Specifically Majesty brand 1.5-1.8# slabs. These ribs tend to dry out easily when smoking, so a short smoke period followed by a "bake and sauce" routine was the preferred method of cooking these ribs in the restaurant world. American style baby backs are much better to smoke as they have more fat, but will still dry out if cooked completely in a standard dry-heat smoker. The best smoker for these ribs is the Alto-Shaam smoke & hold device, which is a commercial chip-smoker. Cooked overnight, it makes some of the best Baby Backs, and some of the worst Spare Ribs, as it provides up to 100% humidity. We used these for Baby Backs and Old Hickory or Southern Pride smokers for Spare or St. Lois ribs. The Alto also makes great Beef Back Ribs and Pork Shoulder.