1 click embedding does support for registered users too. If you share a dashboard with single users/groups/entire enterprise, only those users can then access your dashboard. they will be challenged to enter their username/pwd for auth.
Now, 1 click embedding, the URL is static and doesnot change. This is recommended when you want to 1/do embedding in your internal applications or 2/ for public facing sites or 3/ a quick POC.
API based embedding URLs generated are 1 time use URLs with limited lifetime, this is important for security when embedding in external facing SaaS applications.