Context
What's the difference between these two modules?
https://www.drupal.org/project/group_domain
https://www.drupal.org/project/domain_group
Discovery
From the Group Domain project page:
Allows accessing of groups and their content on a different domain (mapping domains to groups).
Similar module:
Domain Group - integration of Group and Domain modules, different in terms of adding everything that Domain has that may not be needed in many cases.
Sounds like Group Domain is a simpler solution for setting up groups as a domain.