The requirements for the Digital Media degree are the same -- complete 9 courses plus a capstone or thesis project.

A thesis is the more appropriate choice if:

you want to get a PhD or other advanced degree and want the experience of writing for publication
you want to work individually with an advisor
you are more self-directed, are good at managing your own projects with very little supervision, and have a clear direction for your work
you have a project that requires more time to pursue

A capstone is the more appropriate choice if:

you don't need or want the experience of writing a big publication
you want more input on your project, from fellow students and other instructors
you want more structure to your project, including more internal milestones and due dates

From the Extension website:

Course requirements

To earn the degree, you choose either a thesis or capstone track, depending on your goals and interests.

Either track requires one on-campus course. See the on-campus requirement.

One computational design course (required for admission)
Two digital media courses
One education and instructional design course
Two web design and application development courses
Three concentration electives
A thesis or capstone

Thesis

In this track, you end the program with a thesis project. You work individually with a thesis director to solve significant software problems and produce documents of publishable quality.

Capstone

In this track, you complete DGMD E-599 Capstone Design Studio, in which you create an individual project and present it to a faculty committee.