Whether someone is a domain admin or a course manager is dependent upon the scope of courses for which you want the user to be responsible.
In the case of a domain administrator, they will be able to operate on any course which falls within their domain, regardless of whether they are registered for it or not. For example, you can give a domain administrator access over only courses in the economics department of the humanities school at the main campus all the way up to every course throughout the system. This is the broader of the two cases and is ideal for people who should have authority over lots of courses and are not actually "enrolled" in them.
A course manager is a user who can administer only courses which they are enrolled in. This could be someone like a coordinator of 15 sections the same course who is also technically "registered" for them. This is the narrower of the two cases.
If you are a system administrator, you can find and set who has domain access by clicking Admin > Users. From there, you will be able to discover who has specific permissions for campuses, schools, and departments. You can also then select specific users to alter their permissions.
If you then want to review administrative options for individual courses, first visit the course and select Settings > Group. You will be able to set the permissions for each course group (instructors, students, etc.).
You can also add users and set their groups by going to a specific course, then clicking Users.