Sharing a receptacle box 220v with a 3 wire and 4 wire appliance
In a code free world, you would need a 4 wire receptacle and two plugs to match. You'd wire the welder with four wires as needed and wire the compressor with the three wires in the other plug and not connect the terminal for the fourth wire. 
I don't think you can't do this. You shouldn't jury rig plugs and outlets like this. The other major problem is the 60 amp breaker. If either one of your pieces of equipment failed, they burn up before your 60 amp breaker tripped. They would literally have no protection.  Do this right and run two circuits, protecting them individually. If this run is in conduit, running two circuits would not be that difficult.