My understanding is that a fly-by-wire system involves computer processing of control inputs in some form, and does not simply mean a control system where control signals are passed electrically (instead of mechanically or hydraulically) directly between cockpit controls and control surfaces as in the case of Concorde. Hence Concorde was not an FBW aircraft.
A fly-by-wire system can use a range of control surface combinations to achieve the commanded manouvre. The pilot can command a number of things- for example in the case of pitch control, can command pitch rate, a vertical acceleration or the traditional elevator deflection, dependent on the control law in use.
At least this is how Bristol Uni are teaching it, I'd be happy to be proven otherwise. Any Airbus types out there?