I'm seeing the following screenshots on the Samsung Galaxy SIII Neo. I would like to know the difference between TouchWiz, TouchWiz home, and TouchWiz easy home.
TouchWiz is the interface used by Samsung, they're including it in their stock ROMs.
"TouchWiz home" and "TouchWiz easy home" are the launchers, supplied with the TouchWiz interface. The "TouchWiz home" is used by default and is more feature-rich.
"TouchWiz easy home" is more basic, made for easier use. It's themed like this: