search engine marketing is more on utilizing the power of search engine to market the product and services that you have in a specific target market. That's my understand on what is search engine marketing.

The process of building and marketing a site with the goal of improving its position in search engine results. SEM includes both search engine optimization (SEO) and search advertising, or paid search.

Temi you are quite right in that SEO (in the hard sense) and SEM have now branched off to cover entirely different practices with some overlap in the activities. Search Engine Marketing (SEM) has now become a large part of Internet Marketing because they share similar aims and activities in publicizing a website to those looking to find its products and services. Much of SEM is now in Social Outreach Marketing (SOM), while traditional SEO is still a nuts-and-bolts approach.

In truth only purists care about these distinctions. What every webmaster really wants to do is get their website high on Google (predominantly) and drive targeted traffic to their website which will lead to successful online conversions in terms of customers/members or subscribers.