Smith & Wesson assigned model numbers in 1957. The K38 Masterpiece became the Model 14. Some called it the Target Masterpiece to differentiate it from the Combat Masterpiece with 4" barrel. Most of us just called it a K38 and everybody knew what we were talking about.
As late as 1975, they were still listing them by both name and number. Nowadays younger shooters and beginning collectors not familiar with model names tend to use such hacks as "Pre-14" to describe the older revolvers.