I would imagine that the circuit uses the auxiliary contacts of the contactor to form a latching circuit.

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To show the principle, I have drawn out a simple version and shown a battery as the power source.SW1 is a momentary press to make, and energises the relay and the first set of contacts form a hold loop. The second set of contacts control your machine. To switch the circuit off you need to break the loop with SW2, which is a momentary press to break.

This circuit also has the advantage of not switching the machine back on if power fails (NVR).

Hope this helps.

Cheers, Rob