In simple terms, the difference between SEO and SEM is given below:
SEO - Search engine optimization (SEO) is improving website visibility in search engines, usually by free methods like following HTML standards and building content.
SEM - Search engine marketing (SEM) is a type of online marketing that focuses on search engines - this can include normal search results but also PPC/paid search placement.
Therefore, search engine optimization (SEO) is a part of search engine marketing (SEM).
PPC Pay Per Click - Advertising model in which advertisers pay for click-throughs to their website. Ads are served based on keywords. PPC model has emerged on the Internet and become one of the leading advertising models in the online world.