Robert, absolutely no difference in the actual firearms. Manufacturers mark certain firearm packages for sale to First Responders usually with an accompanying discount over standard firearms packages as a token of appreciation for their service. budsgunshop.com/index.php/cPath/1799/Qualified+Professional+Discounts

Robert, Basically No difference. Complicated answer to this question. Mechanically there is no difference, but military and police contracts had different specifications of features for each contract. The M686 was acquired for law enforcement and special forces uses by several others nations. The present model was designed and produced in 1980. The 686 has several nicknames for what service and country. NICKNAMES
Distinguished Service (M581, M681)
Distinguished Combat Magnum (M586, M686)
Mechanically and operationally there are no differences between the M686 and civilian 686. The Smith & Wesson Model 586, is a six- or seven-shot double-action revolver chambered for the .357 Magnum cartridge. It is essentially the same weapon as the Model 686, the 586 has a carbon steel construction and is available in a blued or nickel finish, while the 686 has a stainless steel construction. the M581 is blued with 4" barrel. Finish, barrel length and capacity for the .357 mag models for military and LE contracts change, but operationally no difference.