There is no accepted technical term called fast jet. However, this seems to be used in media and other uses, especially in the case of British jets. Most of them seem to refer high speed aircraft (BAE hawk, for example). This conference to be held in London, for example repeatedly refers to fast jets:
BAE Systems provides cutting-edge electronic avionics systems .... Its display systems offer fast-jet pilots a real-world view...
AMPA is used extensively across the RAF from fast jets and helicopters ... (A) pilot following the Fast Jet training system will use AMPA at every stage of their training involving Tucano, Hawk T1 and Hawk T2 aircraft before moving on ...
The British seem to use it regularly, for example for the Hawk advanced trainer:
BAE Systems ... said, “... increase the Indian Air Force’s fast jet training capacity and establish a similar fast jet training solution for the Indian Navy. The Hawk AJT fast jet training solution enables an Air Force or Navy...
My guess is that the usage of term is mostly found in UK (the book also appears to be from there). There doesn't seem to be any consistency in usage. While the examples above include the Hawk among others, another media report (UK again) refers to Dassault Rafale as a fast jet:
French Navy Fast Jet Duo set to thrill Air Day Crowds...
To reiterate, I'm not aware of any precise technical term called 'fast jet' and this seems to be (mostly) a British thing.