[1] Mains power (called household current in the US) is universally AC.
Most mains-powered electrical equipment, though it may specify a single nominal voltage, actually has a range of tolerance above and below that point.
Others use an external power supply comprising either a transformer and rectifier, or electronic circuitry.
Switched-mode power supplies have become widespread in the early twenty-first century; they are smaller and lighter than the once-universal transformer converters, and are often designed to work from AC mains at any voltage between 100 and 250 V. Additionally, because they are typically rectified to operate at a DC voltage, they are minimally affected by the frequency of the mains (50 vs 60 Hz).
The output frequency and waveform of an inverter may not accurately replicate that supplied by mains electricity, although this is not usually a problem.