Let's go over the fundamentals, and I think that will answer most of your questions.
An ordinary generator consists of a small gas engine direct coupled (no belt or chain drive) to an alternator that puts out ac current. In order for it to put out 120 volts, and more importantly, 60 cycle electricity, it needs to run at a fixed speed, usually 3600 rpm. If the rpms on the genny fluctuates, so will the voltage and the cycles - you might get 105 volts at 57 cycles, or something like that.
Since it has to run at the same speed regardless of the electrical load on it, this would be the same as if your car had to run at 4000 rpm whether it's going 10 mph or 70 mph.
Now, an inverter generator starts out with the same small engine and alternator, but the output of the alternator goes through a bank of diodes to convert it to dc, just like the alternator on your car. A built in inverter takes that dc and changes it back to ac current.
Since the inverter is creating 60 cycle 120 volt ac from the genny's output, the genny no longer needs to race along at 3600 rpm at all times, it can throttle back to low rpm when the electrical load is low. This is why the inverter generator runs quieter, and why it runs longer on a tank of gas. Even though it costs more to add the diodes and inverter to the generator, it will more than pay for itself in fuel savings over it's lifetime.
Now, a few other bits of information
A 2000 watt generator is not capable of putting out 2000 watts CONTINUOUSLY. Usually it's good for 1600 watts continuous, with brief periods of up to 2000 watts to start loads like air conditioners and refrigerators, where the starting load is higher than the running load.
All generators are rated at sea level. As you go up in elevation, all gas engines lose power, including the ones on your genny. A genny that might be capable of running your A/C in Florida might not be capable of running it at 10,000 feet in Colorado.
With Honda, and Yamaha generators, and, I guess Champion and some of the others I'm not that familiar with, you can hook a sync cord between two of them and pull double the output out of the pair via a single power cord. In other words, two 2000 watt gennies synced together turn into a 4000 watt generator. It costs more money to do it that way, but it's easier to handle and move the two separate units than it is to handle or move a much heavier 4000 watt generator.
Finally, Honda is the only one I know of that uses a fuel pump. The rest, AFAIK, all use gravity feed. With the Honda's, you can get kits that let you draw your fuel from a much bigger fuel container. I've seen adapters for 5 gallon jerry cans that let you convert them into fuel tanks for the Honda. With a setup like that, you could easily let the generator run all night while it provides power for an electric heater you are running in you rv to keep it warm.
BTW, Honda has just discontinued their 2000 watt gennies and replaced them with a 2200 watt model.
Hope this answers your questions.
