There is a regular and a special draw for nonresident elk, deer, and antelope in Wyoming. The licenses are exactly the same, but the cost of the special permit/draw is quite a bit higher. Wyoming has used this strategy to improve the odds in the special draw, working under the presumption that fewer applicants are willing to pay a higher price, thus increasing odds. As previously noted, once you draw the permit the regular and special licenses are exactly the same.
60% of the nonresident licenses for each hunt are given to the regular draw, 40% is given to the special draw. There is no special draw for bison, moose, mountain goat, or bighorn sheep.