"Does changing gear relation produce different speed at same applied power?
Short answer, no.
Torque is the force we put to the end of a lever that is, say, about six inches long, the pedal crank arm.
Torque in English units of old was expressed in foot-pounds. It is a force, not a power, until movement occurs.
How fast goes the movement, times the force behind that movement, equals the power developed.
I am expressing these things in homely words. You will now understand to look upon the gearing not as wheels of a radius, but levers of a length, and when one is levering against another, the common denominator by which to find the force is the effective lever arm length working to move the load.
The gearing transforms torque but cannot change power. Power is the product of torque and speed.
Our human muscle force is at its greatest at zero velocity. Put a suitable length of lever under the foot for the job at hand: to start, perhaps a rather long lever to get us going promptly, say when starting a hill. Then, as speed is achieved, the leg's up and down stroke, which does not produce as much torque at higher rates of reciprocation as when it is stationary but pushing its hardest, is put back into the zone of power efficiency potential of the human machine by gearing up, using a shorter lever (so to speak), the smaller diameter driven plate, as you would call it.
The FORCE is what gets us going. Our force is at basis a reciprocation of one leg pushing, then another, much like the piston of an engine. Our power is that force times its rate of repetition. Our rpm (reciprocations per minute, you might say) range is limited. We use gearing as you know, to optimize the power potential of the human engine by keeping it working within its effective range of rpms. Our torque varies with the pedal position much as does the piston connecting rod of an internal combustion engine.
The gear ratio does not in itself produce different speed at the same applied power, period.
Can defense of the bold statement be simplified? "Gear inches"...copying now from Wikipedia: "Gear inches is one of [the] several relative measures of bicycle gearing, giving an indication of the mechanical advantage of different gears. Values for 'gear inches' typically range from 20 (very low gearing) via 70 (medium gearing) to 125 (very high gearing); as in a car, low gearing is for going up hills and high gearing is for going fast.
'Gear inches' is actually the diameter in inches of the drive wheel of a penny-farthing bicycle with equivalent gearing..."
Back in the day of the Ordinary bicycle a rider desiring speed rode as big a wheel as his inseam would allow. He literally geared UP. Could he go faster on a 60-inch-tall wheel than he could on a 52? Probably, but only because he could not spin the 52" wheel at a sufficient rate by which to develop the power he could develop at lower rpms on the literally-tall geared 60" bike (remember, our human torque/push pressure falls off with increasing rpms). But, if he could spin fast, he could go as fast on the 52" wheel as on the 60" wheel. Other factors being disregarded for this hypothetical example from 1880, you will see that both wheels (bikes were called wheels, then) would travel at precisely the same speed if equal power were applied.