Since the remaining chapters of the Chamber are already open, we now have almost full knowledge of the difference and similarities of the Hover Charm and the Levitation Charm. I've done some thorough research and all my thoughts are now ready to be shared. So to start off, let me CONFIRM tha the Hover and Levitation Charm are different spells and have different incantations. All my information comes from Pottermore. So, to prove that these are different spells, please refer to the following 2 links:
Read the end of the links attentively. The hand movements of the spells are different, which indicates that the spells themselves, and the incantations as well, are different. Next, the names of the spells are known. The Hover Charm and the Levitation Charm. The canonical incantation of the Hover Charm is unknown. We have the "Wingardium Leviosa" incantation. I can now prove that this is not the incantation of the Hover Charm. This is the incantation of the Levitation Charm, mentioned on Pottermore and HP books. If you view this page from the Pottermore website, you can see the name and the hand movement (swish and flick!) of the Levitation Charm: http://www.pottermore.com/en/spells/the-standard-book-of-spells-grade-1
Now, please view this page: http://www.pottermore.com/en/book1/chapter10/moment2/levitation-charm
If you add that spell to yout favourites on Pottermore and view it in your "Favourite Spells" tab, you can see that the hand movement of the Wingardium Leviosa spell is the same as the hand movement of the Levitation Charm from the "Standard Book of Spells: Grade 1" section of the "Spells" part of Pottermore... It remains, that we now only need to know what is the incantation of the Hover Charm, to close our circle of this topic.
Seems like I finished! I hoarded my thoughts and ideas about these spells for many years. I'm a very big Harry Potter fan and I have keen eyes on such things. :)