What should be the process for documenting design decisions in a living style guide?
The short answer is both, which lends for documentation at two levels:
1.) Documenting Design Patterns. These are solutions to a common problem, and are used as a reference point. For example, using a captcha to verify that content is being submitted by a person and not a robot is a common UI pattern. However there are many ways how this pattern can be implemented (like using images, vs sound, or both). So one level of documentation can include indicating that this is pattern that you would use in your app in certain scenarios, and then there would be a more detail level of documentation that would describe how.
2.) Documenting Styles and Components. This is the more detailed information about how design patterns are implemented in your app, and should include UI, UX, accessibility guidelines as well as coding standards and specific direction on how to implement the style or component.