In order of least severe to most severe, here are some of the actions moderators can take. Much of this is described in that moderation documentation.
Without recording a strike or anything, we can just DM them and say “please knock it off” or get more information about what they were doing.
There's a strike system and warning system that all moderators have access to. We can issue a warning to a user, which is visible to current and future moderators.
Marks all posts from the user, regardless of content, as sensitive. They can post all they want as much as they want, but it will always be marked with a warning.
A limited account is hidden to all other users on that instance, except for its followers. All of the content is still there, and it can still be found via search, mentions, and following, but the content is invisible publicly.
An account limited here is still visible and federated on other servers. Account limitations are reversible.
This only works on OUR users. The user can't do anything with the account, but all of the content is still there untouched. This limitation is reversible; the account can be un-frozen at any time.
Suspension means the account is effectively deleted. The account no longer appears in search, the profile page is gone, all of the posts, uploads, followers, and all other data is removed publicly.
If they're not our user and we 'suspend' them, it's blocking that individual user at our server. Their posts won't appear in our user's timelines and our users can't follow/interact with them.