They use different methods of putting heat into water.
A microwave turns the electricity into RF radiation that is absorbed by the water. To produce that radiation, the input electricity is converted to thousands of volts by a DC power supply. So regardless of whether it's 120 or 230 input voltage, it all gets converted to the same high voltage DC to run the magnetron.
A classic electric kettle works by running the current from the outlet through a resistive heating element. Double voltage means double heat.
Induction heaters use a power supply to reduce the input voltage while increasing amps and frequency to heat metal through inductance. So, similar to a microwave, the voltage of the outlet is largely irrelevant.
Tl;Dr: microwaves and induction heaters change the supplied voltage to function, so they work the same in UK and US; resistive heaters work faster on 230v like the UK uses.
Because resistive heating is inefficient. You need to pump a lot of power through to get a lot of heat. A microwave does not use resistive heating and works on a completely different principle and therefore the amount of power available is much less importance.
Resistive heating is almost perfectly efficient. Where else would the energy go? Using a hot piece of metal to heat water might be slower than using microwave radiation, but that's a different kettle of fish.
Yes all the energy goes into being heat but you have to put a lot of energy into the wire before it heats up. Microwaves barely use any energy in fact it takes more power to run the little clock than the microwave itself.
That's insanely untrue. Microwaves are power hogs up to a 1000 watts or more in some cases. The difference is the heat transmission method. The conduction of heat in a kettle is pretty slow because it forces the heat to propagate through water via convection, which is slower, while the radiation of a microwave antenna distributes the energy more evenly and faster. Consumption is mostly on par but energy transfer differs.
Yeah, but not for countertop appliances. Those are all 110/120VAC. Even things as large as a consumer level refrigerator or freezer are almost always 110/120VAC too.
While I have a kettle for water, there are two issues with them for tea.
The water gets stale and the reheating drives off the all the excess air that fresh water has. This loss of dissolved oxygen kills the flavor of your tea and makes it taste bad. You should always use fresh water to make your or even coffee.
A cheap kettle is, well cheap. You can't make a good cup of green or oolong tea if you pour boiling water on it. Those need to be brewed at a lower temperature. And guessing doesn't work. And a temperature adjustable kettle will set you back anywhere from $50US to $100US.
A microwave does not use resistive heating and works on a completely different principle and therefore the amount of power available is much less importance.