How is the steepness of turn bank properly defined?
I don't know if this is only definition out there, but according to the FAA's Airplane Flying Handbook:


  Shallow turns are those in which the bank (less than approximately
  20°) is so shallow that the inherent lateral stability of the airplane
  is acting to level the wings unless some aileron is applied to
  maintain the bank.
  
  Medium turns are those resulting from a degree of bank (approximately
  20° to 45°) at which the air- plane remains at a constant bank.
  
  Steep turns are those resulting from a degree of bank (45° or more) at
  which the “overbanking tendency” of an airplane overcomes stability,
  and the bank increases unless aileron is applied to prevent it.