The Itouch Phone is the most common reference and it refers to the apple Ipod Touch being used as a phone from using Applications such as Skype, Fring, Viop Buster etc. With this they can buy an Ipod touch and then be able to call and SMS other phones for free using Wifi.
The main reason that this all came about is when users were against paying the few hundred dollars to get an Iphone instead of an Ipod Touch, they felt as though they should just get a separate Ipod, Phone and Digital Camera so that if one breaks you wont lose everything. Unfortunately over time people started seeing the beautiful pleasure and glory of having a phone on your Touch Screen Ipod and tried to create one themselves. This is how the whole "Ipod Touch Phone" came about.
The two main ways of turning your Itouch into an Iphone is through using the free Skype application (Downloaded from the app store) or using Downloading Fring from the Appstore and then using VOIP Buster on your computer. Fring will turn your ipod into a real phone and will give you a free Phone Number where as Skype can call people but you have to pay to get Voice Mail, a phone number, etc.
A problem with this idea is that the Ipod Touch has no microphone - but that can be perfectly fixed by using a splitter to connect an average pair of computer Headphones/microphones into one socket, by buying a non-wireless one ear piece, or by buying proper Apple Earphones from an apple store that are currently valued at $35 (These are just earphones with a microphone on them, they dont have a Volume button or anything). Rumors also state that Walkman and Motorola also have a similar thing but the ends don't fit correctly into the ipod socket.
Another problem that is occurring with the Ipod Touch Phone is that it can only be used in an area with free Wireless connection to the internet, therefore this phone could only be used in places such as Home, School, Maybe Work, Macdonald's, Starbucks, Apple Stores, etc. But most people believe that its perfect to have an emergency phone in case their phone is out of battery or runs out of credit etc.
Person 1: Oh crap! How can Bob pick us up from the airport if my phone is out of battery and there are no pay phones near us?
Person 2: Its ok, lets just go to Macdonalds and use their free Wifi to call Bob on your Itouch phone!
Person 1: Hey thats a great idea! Thank you Person 2!
Person 2: My pleasure Person 1.
Person 1: Oh Noes! I just broke my skype phone!
Person 2: Thats ok, just use skype on your itouch!
Person 1: OMGZ It works!