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.