A token is something you are given so that you can give to someone else. A cookie is a token where the "someone else" is the person who originally gave it to you.
> it sends that cookie to you as part of a URL in the confirmation email
This certainly isn't a web cookie in the sense that I'm used to (a cookie would be a part of the HTTP header, and you can't specify that header in a URL). It is more like a token as I understand it. Maybe what you are describing is how the web cookie term was started (based on the behavior of generating a thing that someone else gives back to you) but it doesn't sound like a cookie at all to me.
I meant cookie.