The ones in mostly lower case are the tables from your 6.x forum. The ones like ubbt_FORUMS are the ones from the 7.x forum. They both have been installed in the same DB, so you're seeing both. Eventually when you get everything working right, you'll be able to drop the old style forums.
If you're adding a forum and it's not showing up, for starters you can make sure your cache is being updated (this holds the information on the forums for the list). At the bottom of the control panel menu you'll see an option to clear the cache. Try using that.
