2 user registration forms
It seems there is not any module that provides this functionality directly. But certainly you can achieve it using other contributed modules.

Profile2
This module allows you to create user profile for the users. You can create profile for the two users like free_registered user and admin_approved users, and can add any number of fields on the user profiles.

Profile2 Registration Path
This module allows you to set the unique registration path for each profile2 user profile.
So after installation you will have two registration forms for each profile2 user profiles. You can access this form from the path specified in Profile2 Registration Path module configuration.


Let me know if any issue occurs. :)