Inverter generator or welder? There are both. I even have an inverter microwave.
Layman version as best as I can make it. Inverters take AC power, and break/chop it down into tiny pieces of DC power and then reassemble it into the wave form with the use of diodes/rectifiers and transistors (usually Mosfet, IGBT, or some sort of thyristors). In essence a big filter that lets power only pass in one direction instead of changing polarity. Most AC/DC welders that are transformers use some sort of rectifier to achieve DC power. Think of an AC sine wave then chop the tops off the sine wave close to the top and discard the rest. Then the top of a long sine wave resembles a long, flat dotted line...which is essentially DC but with some gaps. Most inverters goes further. It chops the tops and bottoms (positive and negative parts) off and "inverts" them to fill in the gaps somewhat. The transistors then takes this and reassembles this wave, into a straight (er) wave form switching at 10's of thousands cycles per second. It is usually then run through some "conditioners" such as capacitors, small transformers or special coils that smooth the DC out even further and creating even more of a straight line. Or it can take this DC wave and turn it back into AC sine wave that can be adjusted to any desired frequency (within reason). All of this is electronically managed of course.
One point I'd mention is that whether an inverter or transformer, you really don't have a 100% true DC straight line "wave". It's chopped up into many tiny little pieces of DC power. It's sort of like having a long line that at regular resolution looks solid, but as soon as you start putting it under a magnifying glass, you can see the tiny little breaks between each part of the line.
The difference in a rectifier system on a transformer welder is the smoothness of the DC and the shape of the AC wave form. The rectifier of the transformer has only 60 cycles per second to operate on and it leaves larger gaps between each component of the sine wave. An inverter provides cycle times is several hundred times faster than that, which can create a smoother, less noticeable gaps in the DC output. A DC generator like an SA 200 works off even a more pure DC output because of it's design. Some of your cheaper modern engine drive welders (cheaper ones) use an alternator basically and then convert it to DC for DC output.
An inverter generator produces AC power first, in 3 phases. The more phases used, the better the quality of power will be put out because there are more sine waves to work with creating a more consistent line of DC that can be converted back into a stable AC output.
This probably got a few errors in it as I am not an electronics engineer...