How to set up cellular for a device under one name with a different plan under the same carrier
How to set up cellular for a family member with their own iPhone and different carrier plan
Apple Watch
If that family member has their own iPhone that is not exactly the Family Setup any more, which means one iPhone and multiple watches.
So in that case it would just be a normal setup. However, you could then take advantage of the Family Sharing features:
What is Family Sharing? - Apple Support
Set up Family Sharing - Apple Support
In Family Setup, you can use different carries for the watches too, as explained in here:
Set up an Apple Watch for a family member - Apple Support
Yes a bit confusing with so similar terms for these two different things...