Although they both use Moodle for a Learning Management System, open.umass.edu is a separate Moodle installation designed for use by MOOCs, open courses, and open communities in which people who are not part of the UMass Amherst community can participate.
Please carefully follow the instructions in Step-by-step: How to open a user account on the front page of OPEN UMass.
Important! After Moodle sends a confirmation email and you click the link in the email, you need to return to your Profile page and click Update profile a second time to create your account. If you still cannot complete the process, please contact the instructor or facilitator for your course.
Technically, you could use either. There are advantages to each:
Primarily, that depends on when the instructor running the course decides to close the course.
In addition, if your open.umass.edu account is set-up using your NetID to login, and you graduate or leave UMass, 6 months later your NetID will expire, and you will no longer be able to log-in, even if the course is still open.