When I did start learning advertising then I often confused this term with marketing. Funnily, the Difference irritates me a lot. (becomes more crucial specially when you are writing your exams ;) and to get Max Marks you need to play with words and that too distinctively different from the bunch of your mates huhh!!!), so after reading form several books and after referring few web-links, finally I have arrived to the following short and sweet understanding which can be further elaborated as per individual's capability of writing skills....:D hope it will help future mAD students... ;)

Advertising: It stands for the persuasion. A component which facilitates marketing. Advertising in technical term is a paid, public, non-personal announcement of a persuasive message by an organization of its products to its existing or potential customers. It is the process of developing strategies such as ad placement, frequency, etc. Advertising includes the placement of an ad in such mediums as newspapers, direct mail, billboards, television, radio, and of course the Internet. It begins with understanding the clients brief and ends up at delivering the executable and impact ful idea to the masses.
Marketing: The systematic planning, implementation and control of a mix of business activities intended to bring together buyers and sellers for the mutually advantageous exchange or transfer of products. Marketing is everything that the consumer encounters when it comes to your business, from advertising, to what they hear, to the customer service that they receive, to the follow-up care that you provide. It’s all marketing and creating the decision within the consumer whether or not to choose you initially or for repeat business.
Here is the Difference: Marketing is a pie, inside that pie there are slices of advertising, market research, media planning, public relations, product pricing, distribution, customer support, sales strategy, and community involvement. It is as simple as that advertising is one piece of that pie in the strategy. Marketing is everything that an organization does to facilitate an exchange between company and consumer and take help of advertising to reach the goal.