How smart thermostat work?

I was wondering how they work since they are connected to a mechanical system (rotation to increase/decrease the heat). Is there some kind of motor inside rotating? All websites dumb down so much the explanation that I can’t put my hand on how they piratically work. Also, for the systems controlling the boiler, how are they connected/commanded?

Thanks for your help!

Model without boiler system in question:

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Original article: How smart thermostat work?
Author: /u/Start0ad