In short, flagging is usually the step that comes before moderating. When you flag a post, our Packback team will review the flagged post and decide to moderate it or not. When you moderate a post, it gets moderated immediately and the student will be notified via emails.
While the "Flag" option is available to everyone in the community (student, professors, TAs), the "Moderate" option is only available for TAs and professors.
Since you're a professor or a TA, we would suggest you moderate the post instead of flagging!