You'll probably get other explanations, but the way I see it is that internet marketing encompasses every aspect of marketing your site online, including email marketing, banner advertising, link exchanges, seo etc.,
Seo is a subset. It's where you focus on making your site search engine "friendly" and then work on getting the keywords / phrases you are focussed on to "rank" well ie. drive traffic and business to your site
In my view the distinction will blur more and more - if I could only offer to get people traffic I don't think I would be offering the optimal service. If I can help people get traffic and convert that traffic into money then I think what I offer is truly valuable.
I have a 4 month old blog post about this very issue. I might get around to actually finishing it some day (along with all the others...*sigh*)