All electrical appliances draw on available current as measured by an electricity meter. The unit of measurement is Kilowatt Hour, each of which costs a set amount of money as decided by both the generator and provider. Each appliance uses more or less electricity than others, and some simply require more electricity to operate depending on size and purpose. For example, a toaster over uses a small amount of electricity in a short period of time, heating up its toasting elements and then shutting off. Because it does not use electricity over a long period of time, and because the amount of electricity used to heat toaster elements is relatively minor, it does not cost much to operate.
In comparison, an air conditioner uses a great deal more electricity to operate, since it must remove heat from air and run a fan; it is also normally kept running for longer periods of time, and so uses more electricity, and costs more money. A hot tub heats a great deal of water, and that heat must come from constant electricity; a radio only uses enough electricity to tune its antenna and convert the radio signal to audible sound, which in comparison isn't much.
It really boils down to the length of time the appliance is on, and how much electricity it draws while operating. A regular freezer gains heat when it is opened, and so must operate to keep the interior cool; a chest freezer gains much less heat, and so operates more efficiently, using less electricity. Smaller appliances, drawing smaller electrical loads, almost always cost less to operate than larger ones.