How is a "fast jet" classified?
In UK Air Traffic Control, the term has particular meaning as per CAP 413 (The CAA Radiotelephony Manual):


  When receiving an ATS surveillance service, certain ex-military
  aircraft types have been granted a CAA exemption from the Air
  Navigation Order requirement to fly at an IAS less than 250 kt below
  Flight Level
  100. In order to alert the controller to this higher speed profile, pilots of exempted aircraft shall, on initial contact, prefix the
  aircraft callsign with ‘FASTJET’ or ‘FASTPROP’ (depending on
  propulsion type), e.g. “Kennington Radar, FASTJET G-ABCD request
  Deconfliction service”. Use of this prefix shall be confined to
  initial contact with ATC agencies for periods of flight during which
  operations at airspeeds in excess of 250 kt are intended. Once
  acknowledged, it will not normally be necessary for pilots to use the
  prefix in subsequent transmissions until making initial contact with
  other ATSUs.


In my experience, Fast Jet will generally be used to refer to pretty much any jet powered single or dual seat (i.e., non passenger carrying) aircraft