Bear:
Stall recovery, as practiced, was a wings level training maneuver from start to finish.
Approach turn stall recovery included reduce AoA and level the wings, followed by power (with minimal delay) followed by climb.
Spin recovery was taught as an ailerons neutral maneuver from start to the end of rotation. You then level wings and return the nose to the horizon, wings level, with caution to Avoid Rolling Pull Out!
While the spin is in progress, we did not teach the use of ailerons to recover from the spin: they should be 'neutral' in those two models of aircraft.
In others, perhaps not. (IIRC, the T-2 was also a stick 'neutral' spin recovery, but I'll defer to those who know on other aircraft models).
NOTE: If you turned with aileron during spin entry, you could enter a spiral rather than a spin. They look pretty similar (though you don't get the clean stall break at entry) with a nose low and rotation about lateral axis.
In a spiral you aren't stalled, thus anti-spin inputs won't recover from a spiral. There are a few dead bodies that attest to same
... which takes us back to the utility of the AoA gauge.
Sorry for the digression. The above doesn't apply to the AF447, swept wing stall. That aircraft accomplished a lazy turn to the right during the stall, but was not in a spin. Ailerons remained at least somewhat effective (early on?) as well as rudder (see the Captian's directions to PF), and it seems from the released info, so too did pitch control.
A few threads back, someone described the stall as "mushy." There does not seem to have been the clean break at stall that I was familiar with in small aircraft.