Hi Nicole - The author role allows the user to edit the proofing workflow (stages, deadlines, etc) and add new versions of a proof (Configuring Default Proofing Roles). The moderator role allows the user to add new reviewers via comment tagging, but they cannot amend the workflow unless they are also set as a Supervisor or Administrator in the proofing permission profiles (Proof Permissions Profiles in Workfront Proof).
Example: We have our designers default as moderators, because we want them to be able to check actions and tag other reviewers without having to check those boxes every time within proof roles.