An inverter generator such as the Honda EU2000i go up to about 2500 watts in the suitcase style (Yamaha) or you can get a roll around 3000 watt Honda. I believe there are many more but those are mainstream. They only spin up to what power demand is needed...hence the inverter. The inverter portion of the generator creates 120v 60Hz and simply commands the engine to spin faster if more demand is needed.
On the flip side, most convetional gensets are either 1800rpm (typicall lugger marine or large mobile units) or 3600rpm (pretty much every gas job out there). Both of these must remain a constant speed in order to feed the correct Hertz frequency into the outlets regardless of load. This is why they waste tons of fuel powering small loads like lights and fridges. They are really only cost effective when at 3/4 to full load. They are also mostly pretty noisy because of this high rpm speed all the time.
That is a high level view of the difference.
You really would not want to power a house off grid with a generator because there is a lot of waste. With the cost of fuel and having to run it round the clock, lots of waste in that scenario. You would really want to use it to supplement an off grid house during high demand times or to charge battery banks which loads the genny up to full load and uses fuel appropriately. This is how most people run them on boats (relatively speaking of course). The only setup I've seen in an off grid house that makes sense is a lugger diesel engine spinning a generator. The engine heat is also used to create hot water for showers and house heat. So all that extra energy that would have just gone into a radiator is now heating the home. Very effective setup if you are into that kind of thing.
