Your iPhone and Apple Watch must use the same network provider, and you must be within your provider’s network when you set up mobile on your watch. - taken from the article below.
If the Watch is set up as a family member's watch under your iphone then they can be a different provider.
In the following the words mobile and cellular mean the same
Set up mobile on Apple Watch – Apple Support (UK)
Unpair and erase the Watch including removing the old eSIM before gifting
What to do before you sell, give away, or trade in your Apple Watch, or buy one from someone else - Apple Support