You will be able to choose from Normal / Hard / Veteran OR Elite. These difficulties do nothing but make the enemies stronger, no loot difference or anything. You can switch around between them at any point, basically by whatever game you join/create.
New Game+ ++ +++ and ++++ are the equivalent of Norm/NM/Hell on diablo 2. The difference is when you enter NG+, you can't go back. Similarly with NG++ +++ and ++++ once you're in, you're in permanently. NG++++ monsters max at level 120. Playing through the NG's will get you to level 100.
You don't need to go to NG+ once you complete the game. You can stay in normal game and do custom maps from the end game map room(special maps with monsters that have unique abilities). This can get you all the way to level 100.
Hope that helps the people who haven't been following RG.