An advertisement is any published material (i.e. something on or in a newspaper, magazine, billboard, flyer, radio, television, movie etc.) which seeks to inform you of the qualities of a product or service. The intent of the advertisement is usually to get you to buy something, but it can be to vote for something, donate money to something, entice you to become active for a cause, or just plain information.
A commercial is any advertisement that is on radio or television. There must me an oral and/or video component for an advertisement to be called a commercial.