Doctor is way simpler. You create categories or headings. Copy paste links to your documentation files (MD) from github.com into Doctor's Dashboard. There is no creating, editing doc content from within Doctor.

It looks to me like Gollum allows the user to use a wiki like interface to create and commit docs in github. Gollum also seems to allow a variety of formats other than markdown when the user is creating documentation through their server.

Doctor sticks to aggregating, categorizing and presentation. Postgres is used to manage document links and categories and not content itself. Doctor lets github do all the heavy lifting on document creating & editing and versioning.