Ken,
What 'makes' a circuit be rated for 15 amp or 20 amp use is a combination of :
- the circuit breaker (easy to check), which is there primarily to protect the wiring (in the walls and such) from overheating and starting a fire (the wire heats up as more current flows through it, because no wire is a 100% 'perfect' conductor and even the relatively small electrical resistance of the wiring causes heating in the wire);
- the wire size (diameter or "gauge", such as 14 gauge or 12 gauge). May be a little harder to tell as you have to look a little 'deeper'. See above about wire resistance and heating and the circuit breaker being there to primarily protect the wire from overheating:
- the 'devices' in the circuit, such as the switches and outlets themselves.
Note that just saying 'Well, if the wire is 12 gauge then it is just fine for a 20 amp circuit" is only partly correct. Long cable/wire lengths need bigger gauge wires than shorter lengths (because the resistance of the wire depends on the diameter/gauge AND the length AND the material of the wire).
So the long answer to your question of your proposed welder on the 120 V circuit and the wiring and circuit breaker is "It depends."
And btw, unless you somehow have some 'weird' arrangement with the outlets and circuits and such, ALL the 120V outlets in a US garage are -supposed- to be GFCI-protected (either by GFCI breaker or GFCI outlet directly or by being daisy-chained off of an 'upstream' GFCI protective device). With some (limited) exceptions, depending on wiring 'era' and the applicable electrical Code in force at the time (such as a "dedicated" refrigerator outlet or maybe a "dedicated" overhead GDO outlet maybe being in the exempted category from the 'usual' "Garage outlets must be GFCI protected" category). YMMV.
As to the 120V welder, such machines can be useful and certainly handy when used within their limits.
As to the circuit breaker requirements for the machine, if the manual says 'use on a 20 amp circuit', unless you are always running the machine with low power output, you may or may not be able to run the machine in a limited fashion on a 15 amp 120V circuit.
Worst-case scenario there, you get 'poor' welds and/or the breaker trips (no welds).
Also be aware that if you try to run a machine (welder in this case) that need a 'lot' of power on a branch circuit and there are other devices plugged into that circuit and using power, you can 'overload' the circuit (breaker trips). If you have a machine that needs all or almost all of the circuit's capacity (breaker ampacity), make -sure- nothing else is using power from that circuit (any other machines, lights, etc, etc).
Poor welds could result if you get a low-voltage condition at the machine (slightly low incoming voltage from the PoCo, possibly in combination with long or longer wiring lengths leading to more voltage drop over the wiring length) which means the machine doesn't have enough incoming power to work correctly.
Some welders (machines) can 'compensate' to varying degrees with lower-voltage conditions at the machine and some can't.
But at some point, the machine needs *** volts and YYY amps of incoming power to be able to work 'properly'.
And a 'small' 120V FCAW machine may or may not be a 'good' choice to weld on a go-cart. That depends a lot on the machine AND the welding wire filler AND and the operator. If the machine and filler (size and 'type') do not enable you to get the 'correct' heat (power) into the actual weld for the size/thickness of the metal being welded, you can get "inadequate penetration" (aka "cold lap" aka "inadequate fusion") of the weld where it doesn't actually melt properly into the base metal and is just 'glopped' on top of it (but may look 'ok' at a glance, especially by an inexperienced welder). So a big YMMV there as well.
