Yes. The 3G model requires that you connect it with a carrier, whereas the Wi-Fi model does not.
Yeah this is incorrect. You do not need to have a carrier subscritpion to use your 3g vita, only if you wanna use it through a 3g service such as At&t in the US. Matter of fact, when I called them about a pricing rqte for it I was told I could just use my phone's mobile hotspot functionality which offered better connectivity and speed and didn't cost me anything extra....so yeah, fuck the 3g model.