A First Production knife is the next to the last version and are marked as you suggest. These runs can be 200, some 500, others 1000, and typically the very first one off the line goes to the owner, but not always. But these are always numbered on the blade. In the final, or full production, the blades are not marked and all of the minor changes and modifications done to make them just right have settled down.
So; First are the concept and R&D samples, second are the prototypes, third are the first productions - all typically marked, then come the un-marked full production models.
Hope this helps and makes sense.