The best way to clarify the difference between SEO and SEM is as the difference between earning traffic and buying traffic.
You can often tell when SEM ( traffic buying ) is at play because you don't get what you want from the search engines.
As an example, as part of playing around with adsense, I've put various ad tags in a few locations on this blog. One one of my pages, the ad took me to http://www.shopzilla.com/8N_-_cat_id--16011700__nwylf--__oid--558586819 which is a search results page for "tdk mojo 256f." I get the "mojo" part of that, but look at the other terms, that scary looking url ( which is a poster child for bad SEO ), and the final results page. None of these things appear related to me