Can I plug a 220 volts appliance to a 240 volts supply? ….. without damaging it!
First of all you must realise that electric power supply voltages aren’t constant. They try to be constant but vary with load and spikes often happen in the system due to many reasons. Thus there is always a margin for electric power supply variation and electric power consumption.
Secondly, if you have a dumb appliance, an appliance that doesn’t have electronics involved, then there is little problem what-so-ever. Dumb appliances usually involve heating or motors. Any increase in voltage will simply result in more heat or speed and be well within margins.
Smart devices need more care. Over-supply and even under-supply (brown-outs) need more consideration. These days, the way power is converted in appliances by electronics rather than transformers then there is a big margin for differing power inputs. Electronically, appliances will select the correct power from quite a range of inputs. Thus a large number of appliances are offered around the world without modification whereas previously they needed modification and demarcation of models.
Smart devices that are sensitive to power do exist. Ideally, computers need a protected power supply to prevent possible corruption. Again, this need has lessened greatly by the use of electronically determined power supplies. Producing a low voltage from a higher voltage is easy these days and it doesn’t matter whether it’s 110V or 240V if you want 19V dc, the common voltage for computers.
I’d be more concerned about modern smart televisions because they are so expensive and you don’t want power frequency or voltage to cause problems. I’d put them on a protected circuit.