Electric power comes into a house through a three wire 220 volt electric cable. The three wires will have black, red and white insulation. Both the black and red wire carry 110 volts AC relative to the white wire, but they're 180 degrees out of phase. So, when the black wire is at +110volts relative to the white wire, the red wire will be at -110 volts relative to the white wire. Similarily, when the black wire is at -110 volts relative to the white wire, the red wire will be at +110 volts relative to the white wire. The best way of thinking about it (which is technically incorrect) is that the power comes from the generating station along the red and black wires and goes back to the generating station along the white wire.
You make a 110 volt circuit by connecting the circuit between the white wire and EITHER the red wire or the black wire. If you put a 15 amp fuse on that circuit, you have a 110 volt 15 amp circuit which is a standard household circuit for lights and fans and such. If you want to make a 220volt circuit for an electric dryer or stove heating element, you put that heating element between the red and black wires. If it's a dryer heating element, then you would put 30 amp fuses on BOTH the red and black wires going to the dryer. Similarily, if the heating element was a stove, you'd need to put 50 amp fuses on BOTH the red and black wires going to the stove. So, 220 volt appliances like your shop heater and welder will have two fuses or circuit breakers; one on each power line going to the appliance. You need to remove both fuses or trip both breakers before all the power is shut off to a 220 volt appliance.
There's a convention in wiring any 220 volt appliance like an electric stove or dryer. I expect your shop heater and welder are special cases of this general rule because they might not need the neutral wire.
The general rule is that on 220 volt appliances, either on the wiring terminal or on the plug or receptacle, you will see three connection points in a row. The white wire ALWAYS goes to the middle connection point and the red and black wires are connected on either side. It doesn't matter which side you connect the red and black to (because in 1/120 th of a second the polarity will have reversed anyhow), as long as white is in the middle and red and black are on either side.
220 volt appliances like electric dryers and stoves will still need a white neutral wire. That's cuz some of the circuits on a 220 VAC stove or dryer will run on 120 volt power. The electric motor in the dryer, for example, uses 120 VAC power. The indicator lights on a stove's console or the light bulb inside the oven will also use 120 VAC power. To make a 120 VAC circuit, you need to connect between the red and white wires or between the black and white wires.
I think what other people are saying is that there aren't any 120 VAC circuits in either your electric heater of arc welder, and so it's not necessary to even have a white neutral wire, and so you can just stick a big wire nut on the white neutral wire to insulate it's end.
But, look on the space heater or welder to be sure. any indicator lights that are supposed to light up when the heater or welder are turned on are likely to run on 120 VAC power, and that means there's a need for a white wire to be run to the appliance as well.
Hope this helps.