I have to respectfully disagree - as part of my standard FADEC s/w cert test, we did a 'double push' GA test - and I don't recall any differences in procedure between the 767 and 747-400/-8.

Then it's an option. Or it's related to FADEC. The last non-FADEC one I flew didn't have it.

Atleast on 737:
TOGA
For takeoff applies fmc thrust setting, and FD guidance,
For approach gives reduced go around thrust giving 1000-2000fpm RoC with first press, or full Ga thrust with second press, and gives go around FD guidance
During windshear pressing toga initiates windshear escape maneuver (different than go around mode)
A/T off, on approach pressing toga will give you go around FD even with oei landing.

same on 737 actually, indeed nice feature

The E170/175/190/195 have TOGA buttons at the rear of the thrust levers. (In addition to go-around pitch/thrust they switch to FMS guidance and arm NAV mode.)
The Fokker 70/100 had them in between the thrust levers and they had to be pulled up to engage (and they targeted 2000fpm climb/200KIAS or 1000fpm if engine-out was sensed). There were almost identical in movement to the idle locks on the Dash 8.

All turboprops I have seen so far had TOGA buttons at the side of the power levers (where jets have their Authothrust disconnect buttons) which makes for a bit of confusion when changing to a jet.

The only Flight Director I ever experienced on a small GA aircraft set pitch to about 8 degrees when the GA button (on the instrument panel next to the vernier-type throttle) was pushed.

The Airbus version seems intuitive but requires a detent or end stop. If there's a fault with the Airbus design it is not having enough mechanical range between IDLE and CLB, causing manual thrust control to be quite fiddly.