i'm not an electrician, but i have been through many homeowner electrical woes, and i've also not got a warm fuzzy feeling from many answers that i have received. without getting too technical i'll try to give you a little information about 120v/240v in layman's terms:
a ground is a ground is a ground. it doesn't matter whether you have 120v or 240v - the ground is only intended to carry electricity in the event of a fault. it is not and should not be mistaken for a neutral wire, even though they both ultimately connect to the same place in most residential boxes. you will often see this as terminology about the neutral and ground being "bonded". ground wires should be bare metal or green coated.
120v circuits require a hot wire and a neutral wire to operate. this is pretty basic - you need to complete the circuit for it to operate. generally the hot wire will be black and white will indicate a neutral, but never assume this without testing, since not everyone obeys the rules. you are still supposed to have a ground wire in this configuration, and it should only become utilized when there is a fault (when something goes wrong).
240v circuits are where people often get confused. in a strict 240v configuration you will have two hot wires and a ground. your welder is a good example of this. the ground will still not be used unless there is a fault, and this is where people get confused. they see two hot wires and assume the ground makes up the return leg, which is not the case. since we have alternating current (ac) the two hot legs are not delivering power at the same instant. when the first hot wire delivers power, the second hot wire completes the circuit and does not deliver power. when the power is alternated, the second hot wire delivers and the first completes the circuit and does not deliver power. 240v hot wires are generally black or red, but sometimes people will use the white wire as the other hot lead. it is supposed to be marked with any color other than white or green, but often people ignore that. this is why you should never take it for granted. my terminology may not be correct here, but it is the best way i can explain it without using too much technical terminology.
many newer appliances such as ranges and clothes dryers are 120v/240v. on these you will find four wires. there will be a ground, a neutral, and two hot wires. in cases like this, the two hot wires will power the heavy duty part of the appliance, such as heating elements or motors. electronics circuits that are designed to operate on 120v will make use of the neutral wire and one hot wire.
in short, if you have a 240v circuit with three wires, you can't get a 120v circuit out of it unless you do it incorrectly and unsafely.
