I was executing a power-on stall, and upon stalling the nose dropped and the plane rolled hard right. I promptly applied left rudder and released yoke backpressure to recover, and the plane recovered normally. However, my instructor told me that I should not use rudder when recovering from a power-on stall, even when the plane rolls one way or the the other. This confused me, because a DPE had told me not to use ailerons when recovering from a power-on stall if the plane rolls one way or other other, so I'm not sure how I'm supposed to level the plane if I can't use either rudder or aileron. Also, I had thought the roll was the beginning of a spin, but my instructor told me that it was not and that we were nowhere near a spin. Can someone clarify the use of rudder (or aileron) on recovery from a power-on stall? And if I'm in a situation where my plane is stalled and I'm rolling hard one direction, if that's not a spin, can someone please clarify what a spin is?
My suggestion right now is do as your instructor says. Next lesson Ask to get a demonstration or try for yourself.
The full answer is to follow the operations manual. Airplane types vary a lot. The 172 is a very benign type as far as they go. A bit of performance has been traded for simple and safe (well) handling. Other types can be quite nasty, given wrong control inputs they bite.
Your instructor is correct.
I've never seen a C172 where the POH actually discusses stall recovery besides saying it's 'standard'. I was taught to keep the airplane in balance using rudder in the approach to the stall, and manage any wing drops with rudder in a fully developed power off stall (I'm in the UK, not sure how the US is different). However, that isn't the procedure for a power on stall. The FAA Airplane Handling Handbook section 4-8 on power on stalls states:
The pilot must promptly recognize when the stall has occurred and take action to prevent a prolonged stalled condition. The pilot should recover from the stall by immediately reducing the AOA and applying as much nose-down control input as required to eliminate the stall warning, level the wings with ailerons, coordinate with rudder, and smoothly advance the power as needed. Since the throttle is already at the climb power setting, this step may simply mean confirming the proper power setting.
In a power on stall if you get a big wing drop the rudder is not going to lift the wing, and coarse rudder movements could stress the airplane, see the AA 587 crash. So balance with rudder, but most importantly reduce your angle of attack with as much forward stick as you need.