What's the difference between the two waves from a physical point of view?
The amplitude of the higher power wave is greater.
If you measured the electric field associated with the stronger wave with a field strength meter, you'd find a higher value.
In the quantum view, that means you're receiving more photons per second from the stronger transmitter, but this is almost never relevant to understanding RF phenomena.
Why is [the distance from a BTS station where you can still use the signal] from the station [with] a 200 W transmitter greater?
Because (to take a simplified scenario) the transmitter emits its power in all directions, not in a tight beam to your receiver. So the further you get from the transmitter, the smaller the fraction of its output power you are able to receive with your receiver. So the power you receive is decreasing as you get farther from the transmitter. This is the famous "r-squared power law" of radiative phenomena. (You'll also find that even if you try to transmit a tight beam, due to refraction that beam will spread and you'll still end up with received power dropping off as $r^2$)
But your receiver has a characteristic input noise, and a minimum signal-to-noise ratio at which it can operate. So when the input power gets too low, it will fail to receive the signal correctly.
Combining those two considerations, you get the reason why a higher-power transmitter can be received at a greater range.