How does a home thermostat system work?

I always thought that the thermostat display box, was wired through the wall and connected to the furnace. I didn't know you can just buy the display thing, attach it to the wall and have it run your furnace and AC and whatnot. So how exactly does it work? I mean, how is it able to control the furnace and... show more I always thought that the thermostat display box, was wired through the wall and connected to the furnace.

I didn't know you can just buy the display thing, attach it to the wall and have it run your furnace and AC and whatnot.

So how exactly does it work? I mean, how is it able to control the furnace and AC?

Thanks.
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