Yes correct.
You have two circuits. One is the wall socket, the relay 'c' and 'no' connector and the heater
The other (Arduino) circuit has its own power supply and its own ground (e.g. 9V battery).
The only point the two circuits "meet" is the relay where the Arduino part is connected to the relay coil which performs the switching.
Check the links I posted above, especially the second one will make it very clear, it has lots of pictures