It's my understanding that the process for putting the silver finish on guns is a "silver nitrate" application. Per what I've read, silver nitrate (a salt type chemical that is used in photography to light sensitize surfaces) is made into a solution and the part is immersed. I don't recall if an electrical field is required, but my memory seems to indicate no electricity is required. Essentially, it is an electroless silver plating process.
I don't know if "silver nitride" is a true technically accurate term or not. But I haven't found anything on it. I suspect "silver nitride" is a bastardization of the other term. However, I have seen where even Browning described their silver finish as "silver nitride", so I could be all wrong on this.