Search Engine Marketing is the website advertising and promotion that you do for a site, like advertising with banners and using adwords to promote your site. It can also entail sponsorships and other contests to promote a site!
Search Engine Marketing has two components 1) Organic, this achieved through Search Engine Optimization and 2) Inorganic which is done through Pay Per Click like adwords etc
SEM ia a way broader phenomenon than SEO (which might or might not include PPC). Internet Marketing is a set of techniques aimed at promotion of a business (sales, brand, Public Relations) through internet means.