A user feed is a list of all of the posts from the people you follow. These are filtered by the latest posts first. Your feed has the standard Connect post navigation for navigating through posts. If you do not follow anyone, you may get an error message stating so.
The explore feed is for finding new posts, new users to follow. There is no filter on explore posts other than the standard NSFW detection. The explore section takes random posts and shows them to the author. The explore section uses the standard Connect post navigation, with one bug: once going back a post, you will not see the post displayed before going back when going forward.
The latest command does exactly what it sounds like: it shows you the latest posts. New posts first. The last command uses the standard Connect post navigation.