Yes correct, though 400v control circuits may be more for an industrial environment where often 3 phase is used and no N present at the machinery.A few motor plates the all suggest the delta is the 230 and Star 400?
Whilst Im on it, can I ask another couple of basic questions
If we were to connect a single phase motor we could us either a 230v or 400 V coil, as the 230v could pull in the contacts, with a neutral to the coil? and a neutral ran through the spare contactor (5)
If it were a DOL (without neutral for the coil A!-A2) connecting a 3 phase motor, the coil would HAVE to be 400V and the coil would connect between Two of the phases.
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Likely operated by higher skilled people
230v control often found and as you say would need a N present.
Not sure what you mean by "Neutral ran through the spare contactor (5)"
Sometimes you need to be carefull switching N with the 3 phase, ideally you need to break last and make first the Neutral, this is not possible with a basic starter and reason lots of stuff is just 3 Pole
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You will also find 24volt control circuits these are often used when there's lots of devices, buttons etc for control and safety of users.
Advantage no hazardous voltage in areas accessible to workers
Coils are interchangeable nowadays and come in a wide range of voltages