Most people will immediately think about email marketing. If you did, you're not wrong. Email advertising is a segment of email marketing. Here's what the differences are:

Email Marketing
Through this form of online marketing, you are reaching people who took an initial interest in you. They may have bought from you or maybe they signed up for your newsletter. Either way, they like what you're doing. And now that you have their contact information, typically an email address and sometimes a full name, you can email them with new products, discounts, updates or even send them surveys on what they thought of your processes. This opens a new world for marketers and allows them to become influential. By sending these emails they are now converting more people than any other platform available. Email marketing converts more people than Facebook, Twitter and Google+ ever will. So let's cut to the chase.

Email Marketing is the ability to email and convert readers into customers by adding value and/or propositions in an email to persuade the reader to buy now.

Email Advertising
Email advertising refers to the ability to advertise inside an email, not the ability to send an entire email as an advertisement. You might be asking, “What's the difference?”. The difference is the primary content of the email. Where email advertising still has an objective and a purpose with an advertisement tucked into it, an entire email as an advertisement is simply emailing a brochure to somebody with no other value. Think of a hand written letter versus a flyer in your mailbox. That difference is pretty big.
As mentioned above, email advertising is a segment of email marketing. You can advertise your brand inside a purposeful email, while skipping passed spam filters, in a non-intrusive manner. And typically, you'll be the only ad in the email – so the spotlight is on you!

Email Advertising is the ability to put an advertisement inside a purposeful email where the primary objective of the email is to communicate.