Other nerds, please correct me if I'm wrong, but fly-by-wire (FBW) simply means the pathway from inceptors (in-cockpit controls) to flight control surfaces has some portion which is electronic vice mechanical.
Mechanical flight control systems can have fancy AFCS effected by servos anywhere along the control pathway, from the inceptor all the way to the pushrod at the edge of the aileron, flap, rudder, etc. The EC725 has a pretty sweet auto approach to a GPS point at 50 ft AGL which makes a mockery of our Seahawk auto approach.
FBW doesn't necessitate fancy automatic modes, but since it's newer, and changes to those modes are (supposedly) easier to implement with just software, you tend to see much more AUTO stuff on FBW systems.