Did they go Model 10 K-frame .357s...... before ordering the Model 20?...... which in turn was canceled for 681s???
Model 20 was the old .38-44 Heavy Duty. You're confusing it with Model 520, basically a Model 28 but with fixed sights. About 3,000 made, rejected by NYSP. Ca. 1980-81.
NYSP (NOT NYPD) used the Model 10-6 in special production in .357. M-10-6 is normally the heavy barrel version of Model 10 in .38. As more were ordered, S&W made it a production model, called Model 13 in blue and nickel and Model 65 in stainless.
After the L-frame guns appeared, NYSP did adopt the M-681 for uniformed use. I think detectives continued to use the M-65 in three-inch barrel form.
NYPD has never, to my knowledge, allowed guns chambered for .357 Magnum. In later years, they also allowed only guns modified for DA-only use. The best was a M-64 variant, the NY-1 version.
NYSP issued normal selective DA guns, as far as I know. I don't know if they allowed privately owned guns. NYPD guns are cop-owned, but must be of the authorized type, usually bought via the dept.
Movies and TV are fond of having a NY or other cop suspended and having to surrender gun and badge. Now, if that gun is personal property, why? I think that in NYC, the idea is that the suspended cop would have no license to own a handgun. They require a Premises permit to even keep a gun at home up there! It's also likely that TV producers think most/all cop guns are issued by the dept.