I have a 220 welder plugged into a 30 amp breaker and a 50 amp rated plug. I just bought a 220 compressor and was wondering if I could make or have made a short cord with an adapter to plug into the 50 amp plug?

You can do anything you choose...
What is your real question?

You might want to stop and think just a tad, here. Just for the record, the nominal voltage is now 240, not 220 but that is not an issue. Motor branch circuits are a different breed of branch circuit.

You have given us only one piece of valid information. A 30 amp circuit connected to a 50 amp receptacle for a cord and plug welder. Perfectly acceptable.

This proposed compressor, does it require a 30 amp branch circuit using 240 volts?

Motor circuits are not calculated the same way a general branch circuit is calculated.

The breaker may be required to be quite a bit higher in amperage to allow for the "Start Inrush Amperage" needed by the motor. Also, a motor conductor is required to be sized at 125%.