Mag. motor starter or contactor?

There might well be, Motor starters are purpose designed contactors that take into account the normal locked rotor surge current. That is why they are rated in horsepower. In effect, the contacts are over-sized to live through the normal starting surges and the abnormal overload currents, till the overloads trip, including breaking the inductive load of a stalled motor drawing locked rotor current.

Current rated contactors have different and often lower peak inrush and interrupting current rating, and possibly lower power factor current allowances during interrupting, relative to their normal continuous rating. An exception is contactors used as part of circuit breakers (substation breakers, for instance) that must break short circuit fault current, successfully. Most contactors have fuses for this function, so they do not have to survive interrupting a fault.

All that said, you are not switching power to a motor, but to a drive (rectifier feeding a capacitor bank, possibly through some inrush control mechanism, with little inductive impulse during interruption), so you need a contactor that lives through that process for a desired lifetime and number of cycles.

As I understand it a magnetic starter is supposed to be wired so if power fails the contacts open and do not re-energize after power returns. If you want to duplicate this with a contactor wire one side of the contactors coils to the OUTPUT side of the contactors contacts. Some means will have to be added to manually turn on the contactor by physically pushing the contacts in. Once powered it will stay on until a switch in the coils power line in turned off or power fails. If power fails the contactor cannot restart because the contacts are now open and to be physically operated again. All the above may be dangerous depending on how you go about it. Wouldn't want to have an exposed contactor so an insulator of some kind will have to project outside the box it's mounted in. Take this with a grain of salt, I've never tried it but have seen it done. It may also violate electrical codes.

By definition, a motor starter consists of a contactor + thermal overload relay.

Basic contactor includes one(1) aux contact normally used as a "Holding contact" in the control circuit.

The "Contactor" portion may be either manual or magnetic operation.

Either way, the thermal overload relay is designed to trip the contactor in the event of a sustained overload, thus releasing the "Holding contact".

Auxilary contacts are exactly that, auxilarily devices under control of the contacto, usually available with 3-4 max..

Lew