These terms are often used interchangeably. Is there any difference the two terms, or is one of the terms subset of another?
No. There is (practically) no difference between VOIP and Internet Telephony, they are pretty much synonymous.
VOIP stands for Voice over IP. IP is, of-course, the protocol/underlying language of the Internet. Voice in this context is the same as telephony. Neither term implies a specific mechanism for transmitting or encoding the voice (ignoring the IP in VOIP which is generic - I'm talking about protocols like SIP, H323, alaw,ulaw etc)
IMHO (and in my region of the word), VOIP is used by people who know what they are talking about, Internet Telephony would be an older term.
In olden days when telephones were there , there existed something called as PSTN (public switch telephone network) which was automated system to route the calls you made through your telephone. (IN DETAIL HERE . And the instruments we used to use that service were different , Few examples are codless , Landline , and few non-voice related - PAGER, FAX
Similarly in internet world the IP Telephony is the methodology to route all the IP messages. The softwares like SKYPE , GTALK use specific technology called voice over IP , because they transmit calls in packet(which have restrictions and relaxations). Other services are transmission sms and faxes, system to PSTN dialing.For details:Read here.