Point to point microwave links don't have to work through walls, have higher power, use much better (more directive) antennas, and might have better receivers. The communication networks also may have other redundant links to deal with drop-outs (thunderstorms etc.). Other than that they are pretty much the same thing.
It's not just a matter of output power. Like DaveE says, I have usually found that Receiver sensitivity is a bigger contributor to range than output power.
The frequencies used, and therefore the path loss also affect the range. Anything longer than ~ 8 miles also requires a higher elevation on the antennas.
As previous answers, output power, Line of Sight and receiver sensitivity do matter. Also the antenna gain. As WI-Fi uses unlicensed 2.4GHz band, there are power restrictions in most of the regions. Typical maximum 1W (30dBm) of actual power and 4W (36dBm) of EIRP which includes antenna gain. That means if 30dBm actual power is used maximum antenna gain must be 6dBm, where as if 26dBm power is used maximum antenna gain could be 10dBm.
Consider you have a highly directional 24dBi outdoor Wi-Fi grid antenna, then your actual power could be maximum of 12dBm, so the maximum power would be 36dBm. That limits the combination of high gain antenna and actual power.
Point to point microwave communication does not come under these regulations. They use much higher actual power coupled with a highly directional antenna.
One extreme use cases is S band satellite communication. S band is between 2GHz to 4GHz and it is used to communicate with Geostationary Satellites at 36000km away.
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