Original stocks were cut using a series of single purpose, very heavy duty machines.
Modern stocks will likely be made using either a manual pantograph carving machine or a CNC machining center. The pantograph copies a master piece. There are a number of factors which affect quality of the product. My experience is dated - I used a 12 spindle North Star machine to make muzzle loading fusil stocks. Keeping good quality control to minimize finishing time was a struggle. Machines of this type are widely used to make gunstocks. Seeing the stock after it comes off the machine tells a lot more than seeing a sanded, assembled piece.
I have no experience with the CNC route. In the US, Jim Kibler is CNC machining a couple of patterns of long rifle stocks. From the photos and user reports, these are incredible. Swamped octagon barrels snap into place.