What is the difference between the Latest, Unread, and Unseen tabs?

For guest users, there is only the Latest tab, which always shows the most recent posts from all the categories that are visible to a user. For guests this effectively means the story sections at this point in time, for users with accounts, this varies depending on which groups you are a member of and which categories and/or tags you have muted.

The Unseen tab is only available to logged in users and is essentially a filtered view of Latest that only shows topics that have had new posts since your account was created.

Unread (and New) are also only available to logged in users and are further filters.

The Unread tab only shows topics that you have in one way or another set to either Tracking or Watching and have read at least one post in. The New tab shows topics you haven’t viewed at least once and were created since your account was registered if you haven’t changed the default setting for when topics are considered new.