There are or may be several factors that affect the operation of the machine and have an effect on the behavior of the arc.
Regarding input voltage, different machines may behave differently if the input voltage varies from 'nominal'. The machine's circuitry may or may not give a differing output (voltage and amperage for the arc) if the input voltage (from the wall outlet/plug) changes or varies. The 'lower' end machines would probably be more likely to behave like this, as the circuitry is more of an 'open-loop' type. Higher-end machines may or may not behave like this.
quick example: Machine is set up and running with 240V input from the wall, and the operator adjusts the machine's voltage and WFS parameters to give a certain/desired arc. Then the machine is plugged into a different outlet where the actual voltage is only 208V (could happen in a business/industrial setting where the single-phase wall outlet circuit is fed from a leg off of the incoming 3-phase supply and thus the actual voltage at the oulet is 208V and not 240V, or there is a lowered voltage because of electrical loads either in the building/plant or at the power-company side of things). Same settings on the machine and now the arc is different because the incoming voltage from the wall outlet is lower than it was before.
Why is the machine behaving differently now? Because the incoming AC voltage is run through various circuits in the welder, the first usually being some sort of transformer that changes the incoming AC voltage from the 200+ V AC (or whatever the incoming AC voltage is) down to a more arc-welding applicable voltage of maybe 15-30V. Still AC voltage though. After going through the transformer, then the voltage is run through the rectifier (diodes) and changed to DC voltage. Then further circuitry may shape and 'adjust' the voltage in different ways as well (capacitors to 'smooth' the AC ripple a bit and inductors/'chokes' to change/adjust how the output DC voltage behaves during actual welding). Some machines may have adjustments for the output inductance ('harsh/crisp' versus 'soft' ) that let the operator adjust (or mess up

) the arc behaviour further.
Some machines have various incoming voltage taps or adjustments that change where/how the voltage is run through that transformer in order to ginve the 'desired' lower AC voltage. If the incoming voltage does not match up with the machine's settings and circuitry, the output results are not what is expected or desired (usually). Chnage the incoming voltage tap or adjustment to match what is coming from the wall (208V versus 230/240V), and the machine and output settings match back up with the original circuitry design better.
As to how different machines have 'differing' arcs, sure. Goes back to the transformers and the diodes/rectifiers and the capacitors and the chokes/inductors inside the machine all affecting how the arc behaves during actual welding (which is typically
NOT just a steady-state DC output voltage, especially for short-circuit transfer-mode wire welding).
Changing the weld parameters (voltage versus amperage/WFS, the actual shielding gas being used if any, the wire parameters/chemistry, etc, etc) all have an effect on how the arc is behaving during welding.
There, clear as mud now?

:dizzy: