It is amazing to me that we still need to have this conversation in an industry which is over a decade old but VoIP does not mean calls on the internet. Of course VoIP calls could traverse the internet but this is only if this is how the network is designed.
Having said that, it is worth pointing out the definition of telephony is the transmission of voice, video, fax, etc at a distance using electrical signals. Thus IP telephony is roughly equivalent to IP communications and neither has to travel over the internet.
Internet telephony on the other hand refers to the transmission of voice, video and/or fax, etc over the internet.