Not exactly. Wattage equals power, but that does not equal work. Work is independent of time. There's a certain amount of work required to, say, lift a piano up 50 flights of stairs, that is based on the gravity, and the weight of the piano. The EXACT same amount of work will be performed whether it is done in an hour, or 10 years. Power will be much higher the faster it is done though.

Wattage = power. Watts are the unit for power.

Power = work/time

work = force x distance

On the bike, you can use each revolution of the pedals as a measure of distance. Time for this equation is pedaling cadence. Double cadence, you're halving the amount of time it takes to bring the pedals around 1 revolution. The force is the force exerted on the pedal. If you double the force, you double the power. If you double the cadence, you double the power.

So yes, if one person is pedaling at 50rpm, while exerting 100lbs of force on the pedal, while another person pedaling at 100rpm while exerting 50 pounds of force on the pedal, power output (watts), will be exactly the same.

As others pointed out, there are other things to consider, but yes power is the same.