SEO is the process of optimizing your web site for the purpose of getting free traffic from search engine.
Optimized web site is more easily understood by Search engine crawlers and this increases the chances of ranking higher in SERPS.
Search Engine Marketing is over and above SEO but it’s only a subset of your overall Internet Marketing Strategy. The diagram below shows the relationship between Internet Marketing, SEM and SEO.
So, SEM is the marketing process with a goal of getting more visibility in search engines either by getting more free traffic (SEO) or paid traffic