From researching my own Living History days in the last Century (20th not the 19th) I can tell you the coats you see Masterson portrayed in, in the pictures you posted, were called Town Coats. They buttoned higher in the front that modern suit coats or sport coats. Full 'Town Suits' were popular for business attire. They featured matching trousers, vests, and coats - the 19th Century version of today's three-piece suit.
Dave