Good question...
http://en.wikipedia.org/wiki/4D_Ultrasound
Given that we cannot even master a 4D world yet we can figure out Riemann's metric tensor... oh, the irony of mathematics!
You are suggesting that 4D is the spatial manipulation of 3D objects through time, and you are right. However, I am suggesting that most people simply do not know this, or are accustomed to (erroneously) referring to 3D as such.
It's not like 3D animation has never been used before as terminology associated with 4D. In other words, people are far more likely to say (and understand) 3D as a catch-all for 3D objects and animation combined than they are to say 4D. I've even said many years ago (when I was really into theoretical physics and such) "this is awesome 4D" only to draw blank stares.
