The equipment grounding conductor MUST NOT be used as a circuit conductor. Under certain conditions, that can be fatally dangerous. If you add an appropriate neutral, properly installed, the plan is fine.

A completely different code section covers welding equipment.

Article 630

Like motor circuits wire size is no longer directly set by breaker size.

My basic reading of 630 says that under certain circumstances wire can be undersized based on the duty cycle of the welder. In a residential setting it might be better to run full sized wire to future-proof the circuit recognizing that the next owner might own a different tool and never look at the wire size.

If the MIG welder doesn't require a groundED (neutral) conductor, then you don't need to use a 4-wire receptacle but in this case you would need to pull 3 wire (+ ground) cable or 4 wires in conduit for a neutral required for the 120v stick welder.