These phones that say they are "Wi-fi".... does that mean that you can connect the phone to your wireless router and not use your plan minutes when making normal calls?

I've been reading up and I'm still not clear. Web browsing is mentioned, as well as accessing other computers/phones/devices on the network. Skype phone calls are also mentioned, but not normal calls.

I want a phone that connects to my wireless router when I'm at home and does not use my plan minutes to make or receive normal calls (meaning not Skype).