What is the difference between Search engine optimization and Search engine marketing?

Search Engine Optimisation (SEO) is defined as the process of building pages in a manner which enables the pages to rank highly in 'algorithmically' determined search results, which are generally displayed on the left hand side of the page. The 'algorithmic' results are independently determined by the search engine's own mathematical algorithm, and are based on relevance to the search phrase. Search engines use complex mathematical algorithms to determine the relevance of indexed pages for a particular search phrase

Search engine marketing (SEM):   refers to the short text advertisements which generally appear at the top or down the right hand side of search engine results. These are often labelled as "sponsored Links" or "sponsored results". These advertisements are generally purchased from Google. Search engine marketing (or, more correctly, search engine advertising) is effectively paid advertising in search engines, where you 'Pay Per Click' (PPC). It is text advertising delivered in response to 'trigger' words typed into the search box. The surfer types in a search phrase, the PPC advertisements which have bid on that phrase are displayed, and if the surfer clicks on a text advertisement they are taken to the advertiser's website