I am totally satisfied with your definition about SEO & SEM. and u explained both very well.
Do you know SEO, SMO, SMM are the Part of SEM, that means these all are the S.E.M(Search Engine Marketing) process through which you can globalize your business online.
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Yes, they are all part of SEM. Right now experts and gurus all over the world are now in agreement that the most effective among them all are SMO and SMM. Apparently, Facebook and Twitter are among the best avenue to advertise your site or your products/services.