How do cars idle at such a high speed but the brakes stop the car?

I have learned a lot about cars from my Bentley mechanic mom and
whatever she couldn't answer I used the internet to find out. I asked her
this recently and she didn't have a response so here I go:

How come cars will idle at lets say- 700 RPMS but when you stop at a light,
I understand the brakes stop the car but if the engine is connected to the
transmission, to the driveshaft then to the differential then to the wheels,
how does the engine stay spinning at such a high speed but the wheels
don't move? I understand the brakes hold the car in place at a light but
what does the engine spin when the wheels aren't moving? Does it
disconnect from the transmission and just spin the flex plate, flywheel or
torque converter? Please explain that would be great!