I believe the "666" on the front is the model number. This particular machine is sold under quite a few names. I really like the stitch dial, so I notice that quite often. I've even seen a pink one, but it was local pickup only - and way too far away!
The engraved numbers are not the model number - as teh model number is specific to the badged name. I believe there is even one like this badged as White. I've seen it with Remington and a few others too. Each "badged name" has a different model number, but they are made by the same company. The stamped numbers are the Mfg identification marks.