You're all forgetting one crucial fact when defining torque (and my old biomechanics lecturer will thank me for this):
Torque = force x perpendicular distance
I wasn't forgetting it at all, I just thought for the purpose of this discussion it over-complicated things, and was largely, if not totally, irrelevant to argue the difference between power and torque.
You are of course totally correct, to work out the torque you need to know the angle to the perpendicular to which it is being applied. Which in the case of a cyclist does matter quite a bit as we can apply a lot more power when the pedals are level than we can when they are upright! But you don't need to know this to explain the difference between power and torque 😉