Apart from a thermostat, where else can a C-Wire go?
Air conditioners need a C wire, too!

That separate cable that is connected to your Y and C wires goes out to your air conditioner's outdoor unit.  It connects to the coil of a contactor inside the outdoor unit that turns the compressor and condenser fan motors on when you want air conditioning and off when the air conditioning demand has been satisfied.

Heat pumps require a fatter cable as they have more wires going to them, and some modern units substitute a control board for the simple contactor found in an older air conditioner as they have a multispeed or modulating compressor and/or multispeed condenser fan.