James is the first person I have been able to share Apple Watch activity with.
The Watch activity sharing seems to use iMessage to allow you to message each other. It also allows you to see each other's activity rings, and sends notifications upon completion of a workout, likely goals too. I haven't noticed anything else.
It looks like you can give someone any of the contact info from Settings, Messages, Send And Receive. I used one of the email addresses other than my ID.
I would assume the phone number would work too, if you want to give it out.