Need to separate Customer Users from Internal Users to ensure proper notifications sent via email

Summary:

We are looking for a way to separate Internal Users from External Users (Customers) so that different notifications gets sent during the user creation and activation process.

Content (please ensure you mask any confidential information):

We are in the process of implementing Bill Management and we have run into the issue that when registering a customer they automatically get assigned to our Default user group. How do we assign Customers automatically to a newly created user group which we created because the welcome email and password reset emails need to contain different information? Or is there a different way, other than user groups, to handle this so that internal users do not get the welcome email but external users do and to ensure the notification with the Bill Management URL only goes to