Here’s a quick explanation I got from the forum software community …
Newest (Discussions): This option sorts discussions based strictly on when the topic was originally created. If you are looking to find the absolute freshest, untouched conversations, you use “Newest”
Latest (Posts): This option sorts discussions based on the date and time of the most recent reply. If you sort by “Latest” (sometimes called “Recent”), you will see threads that are actively being bumped or commented on right at the top, even if the thread itself is quite old.