It's easiest to see the difference between these two functions if you click "Forums > Mark Forums Read" then come back in 30 minutes and click "Forums > New Posts" and "Forums > What's New".
"New Posts" shows only a list of unread threads with post activity since your last visit.
"What's New" shows all post activity in reverse chronological order, including read threads. Threads with new post activity are indicated with bold titles.