Anemometer is just a generic term to mean measuring wind speed. I've seen many different methods use in projects over the years.
Use a small DC motor as a generator and measure the developed voltage to determine speed.
Use a magnetic sensor to read the spinning cups and time the rpms to determine wind speed.
Use four sensitive RTD temperature sensors along with a reference sensor (not subject to the wind) and with enough software, wind speed and direction can be calculated. No moving parts required.
Use four ultrasonic sender and receiver units and determine wind speed and directions. Again no moving parts required.
I'm sure there may be even more methods, but you get the idea.
Lefty