I don’t see this difference between voip and ip telephony that this company told you about. I’ve never heard of any standard that defined these expressions that way. And even if this was true: why should ip telephony be half duplex then?
Just another idea that comes to my mind when I read what you are writing from this company’s point of view: when I said that there was no difference I meant that there is no difference in the technical realization and technical interpretation of these expressions. If one looks at it literally (and less technically), one COULD define the following (although I WOULDN’T define it that way): “ip telephony” COULD mean that the corresponding subscribers both use IP-based hardware or software telephones, respectively. “voice over ip” COULD mean that the voice data are carried over an ip network but one or both subscribers don’t mandatorily use ip phones (but conventional phones connected to the ip network by the use of gateways).
But as I said, I WOULDN’T define it that way from a technical point of view (my boss doesn’t either, and he’s a professor for telecommunications).
Just another thing: You were asking for the difference between “voice over IP” and “IP telephony”. And I said that I don’t see any. Both express that voice is carried over ANY ip network. This might by the internet but it’s not mandatorily the internet (could be a company LAN for instance).
If you say “voice over internet” or “internet telephony” respectively, these expressions mean that the global internet is used to carry packets that contain voice data. So in fact there is a difference between “voice over ip” and “voice over internet” or “ip telephony” and “internet telephony”, respectively.