seo = it is stand to search engine optimization basically Organic SEO. sem = it is stand to search engine marketing basically pay per click campaign advertising.
SEO=Technique to optimize your site with respect to Search Engine SEM= Marketing technique and also PPC included in it. SEM in the advanced form of SEO.
SEO = search engine optimization organic method, low cost, increasing PR, link building, SEM = search engine marketing inorganic method, high cost, more visitors,
SEO - process of improving the visibility of a web site in search engine results. SEM - is the process of gaining traffic from or visibility on search engines.
SEO = Search Engine Optimization SEM = Search Engine Marketing Search Engine marketing (SEM) is an 'instant gratification' advertising media. You can basically set up a Google Adwords campaign in half an hour - and often have your advertisements running within the hour. Try that with newspapers, TV or radio! You don't have to make any changes to your website structure or architecture. Search Engine Optimisation is a longer term approach, and encompases many 'best practice' web design standards. There are often no payments required to the search engines, as the major search engine spiders (robots) visit your site for free.
They both are large terms and it's not easy to describe here so you can follow the link that has been provided by "mrphantaun".. In short I just want to tell you that SEM is a broad term and SEO is just a part of SEM..