The 586 was made in carbon steel, with either blue or nickel finish (far fewer were produced in nickel, typical of S&W production), while the 686 was made of stainless steel. Far more 686s were made, as stainless was, generally, a better seller than carbon steel at the time the 586 was produced, and S&W was transitioning to producing only stainless steel revolvers during that period. Production of the 586 ended some time in the 1990's, as I recall, and the 686 remains in production. Both are extremely nice guns. I owned several 686s during the 1980s, and currently have a 586, blue, 6" barrel. All are very accurate. My LGS had a pretty nice 4" nickel 586 come in a few weeks ago, but they also had a near-perfect 6.5" nickel 29-2, and I exercised a great deal of restraint in buying only the 29. Went back a few days later, and the 586 was gone.
Best wishes on finding your gun, you will enjoy it, I'm sure.