Oddly enough, cheap generators are pure sine wave, expensive ones have inverters that may be modified sine wave (or worse).
The cheap ones simply spin a generator and easily get a PSW.
The problem is voltage regulation. Switch a heavy load off and there is the risk of a voltage surge that might fry the electronics in your fridge (for example). Put a large load on and the voltage will drop, so they tend to be set to run at about 228v so it won't go too low on load, too high on load drop. But it is a compromise.
That's why they make
inverter ones, which can regulate the output voltage (and frequency) better,
but unless you pay a lot, it won't be pure sine wave.