According to wikipedia
Marketing is a social process which satisfies consumers' wants. The term includes advertising, distribution and selling of a product or service. It is also concerned with anticipating the customers' future needs and wants, often through market research.
Basically marketing is the wide range of activities that involved in the process of continuing to meet the needs of your customers and getting appropriate value in return.
According to wikipedia, the definition of search engine marketing or SEM is
Search Engine Marketing, or SEM, is a form of Internet Marketing that seeks to promote websites by increasing their visibility in the Search Engine result pages (SERPs). SEM methods include: Search Engine Optimization (or SEO), paid placement, and paid inclusion.
In general, Search engine marketing (SEM) refers all the activities that you, or the company assisting you, might do to improve your online visibility.
Then what's the difference between SEO and SEM?
Search engine optimization refers to process of making your site work in compliance with the current ranking algorithm standards of search engines to rank high. SEO is a part Of SEM that only includes organic aka Free ways to increase ranking in search engines whereas SEM involves in free as well as Paid ways to do the same job.
So which one is best to chose SEM or SEO?
If you have enough free time i.e. you are not in hurry to gain visitors and ranking than you can go with SEO but if you want results in short period of time than you better go to SEM.
Although SEO and SEM serves almost the same purpose, it is always recommended to have both working for you to achieve maximum results.