After searching around the internet for other cool animated gifs I found out that there is an actual artistic term for some of the really superb motion images. It’s called cinemagraph. Just do a Google search for the word and you’ll find some really interesting images. I guess that new favorite site of mine can be seen as cinemagraphs while the few images I have created can simply be called animated gifs.
High class animated images = cinemagraphs
Low class animated images = simple animated gifs
Even Lifehacker recently posted a pretty extensive, and difficult to follow, How To on how to create a cinemagraph.