What unit is commonly used when measuring the energy rating of an electrical appliance

usually it is watts

The much more common rating for an appliance is Power.

Power is the rate at which energy is used. Small appliances ... like toasters and blow-driers ... are rated in watts. Large appliances ... like industrial electric water boilers, electric construction cranes, and elevator motors ... are rated in Kilowatts (1 kilowatt is 1,000 watts). This is the RATE at which the appliance uses energy. You leave it running longer, you use more energy, and you owe more on your electric bill.

Some appliances are advertised and sold with an energy rating. This is the amount of energy it would consume if you used it the way a normal standard person uses it, for some standard amount of time like 1 month or 1 year. If the appliance does have such a rating, it'll be in units of Kilowatt-hours. But it'll be no better than a rough estimate, because you may use the appliance more often or less often than the normal standard person.