Power circuits are necessary to supply equipment such as boilers, refrigeration units, heat pumps, electric pumps etc., and the command circuits used to control, regulate and manage such systems. Control circuit is also used in electronic circuits, which may include gate and biasing circuits etc. to control main circuit parameters.
Simple (/rough) explanation with biology background : Control circuit is like brain, it does have lot of logic for operation! Power circuit is like muscle power. It does things but under some one else’s command (brain/control circuit).
Control circuit and power circuit are galvanically isolated and separate. Control circuit links to power circuit by magnetic (relay) or optical coupling.
In Motor starter wiring diagram, a motor starter coil (M) is wired in series with a normally open, momentary Start push-button, a normally closed, momentary Stop push-button, and normally closed overload relay (OL) contacts.
Most common equipment has control units in Electrical panels. Before PLC (Programmable Logic Controllers), control units were like above example and much more complicated in wiring, protection, repair & maintenance, etc. and difficult to develop. PLCs are industrial digital computers which have been ruggedized and adapted for the control of manufacturing processes, such as assembly lines, or robotic devices, or any activity that requires high reliability, ease of programming and process fault diagnosis.
Nowadays, primary studies are about Power wiring and Control circuits. PLCs related subjects are advanced studies in industrial electrician’s courses. Developed processors with more integration capabilities have possibility and power to replace old/slow control circuits.