Welder with GFCI question

The only stupid questions are the ones you should have asked, but didn't. (The ones that result in blowing something perfectly good up because you didn't know the right way to do it.)
I'll take an educated guess that the 14-50R 50A 120/240V 4-wire GFCI protected receptacle you want to connect the welder to is there for a portable spa, right? (That's the only reason to GFCI protect a receptacle - the welder is inherently isolated by it's internal transformer.) As long as the house and receptacle half is wired right, you only have to worry about the load devices.
Check your welder's wiring schematics, or pop it open and trace it out. The welder can not have any 120V parasitic loads hooked up to use the ground wire as a neutral return wire (control boards, cooling fans, work lights, gas solenoids, etc.) or the GFCI will see the current imbalance and trip. Those loads need to be kept separate from safety ground, and go back to the Neutral lug of the receptacle, and to the GFCI breaker neutral load wire.
If the welder is wired for a normal 3-wire 240V receptacle, they probably wired it to put the 'neutral' side of any parasitic 120V loads on the ground wire. If it has any 120V circuits inside you will have to open up the welder, install a new 4-wire range cord with a molded 14-50 cord cap, and switch those neutral wires to the neutral on the new line cord. Chassis ground (the green or green/yellow wires) will be the only thing hooked to the ground wire.
(You might need to use a #10 or 1/4" screw and nut to bolt the neutral connections together to the line cord white wire (and tape them thoroughly) if the terminal strip inside the welder only has two lugs and the grounds go to a screw on the chassis.)
And when you put in a dedicated welder receptacle in another location, you don't need the 50A GFCI Breaker unless you plan to plug your spa in there, too. They still aren't cheap (though they've gone down a lot now that they're required for all new spas).
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This might be a stupid question, but if I want to use my welder on a
GFCI outlet and have it use the GFCI do I have to wire the 3 prong
welder plug so it uses the neutral plug and not the ground plug? It's a
14-50R outlet.
Thanks