Apple Watch actually has its own phone number, but through carrier magicry, calls get routed to both phone numbers (really isn’t too different from a call forwarding system). And then when you make calls out from the Watch it’ll caller ID spoof so that it’s not the actual phone number on the Watch but your phone number on your iPhone (Not really spoofing because you still own the number it’s using, but it’s the same idea, use a different number than the actual number).
Also I think SMS doesn’t actually go to the Watch either, it just syncs SMS over data to your iPhone, I don’t think you can do SMS in the usual way with the Watch (sending and receiving directly). What’s hilarious is that I use AT&T and to use 2-factor sign ins on their app they give an option to send an SMS to my Watch phone number, but that SMS never reaches my Watch, it just goes to a black hole. So I have to make sure I have my iPhone phone number set for 2 factor.