Off topic, inverters / rectifiers

Hello,

Since so many of you on here know a lot about electronics I was
wondering if you could explain something for me. I an thinking about welders
and how MIG sets, the cheaper ones, have a number of preset current
settings. But on DC TIG welders with an inverter they have an infinite
control of current through a thyristor. Are the cheaper MIG sets controled
by a rectifier that just cuts off the top of the ac waves and sticks it on
the bottom? If that's what a rectifier does then how is the inverter
different? I have seen bridge rectifiers and understand they use the four
diodes in that 45 degree pattern to cut the waveform up. I'm sorry it's off
topic but you are the people I'd expect to know about this.

Thanks,
John