If a user can vote to close, they can no longer flag to close (such flags will be automatically converted to votes). But there are more types of flags than those: Spam, Offensive, Not An Answer, Very Low Quality, free-form flag for mod attention, and various flags for comments. All these count toward Marshal. The Help Center page on flagging has links to usage guides for each of these flags.
Having earned the Marshal badge on several sites (Mathematics, Stack Overflow, Stack Overflow на русском, Android Enthusiasts, Drupal Answers, and Meta Stack Exchange) I can observe that the distribution of flags differs by site:
- Drupal Answers and Meta Stack Exchange get a lot of spam
- Android Enthusiasts site is flooded with non-answers posted as answers
- Mathematics and Stack Overflow sites are more balanced: there is a bit of everything. There are offensive posts to be deleted, there is spam, a lot of questions-posted-as-answers, and comments that should never have been written. Flags are used to deal with all of this.