Search engine optimization or just SEO - Can be described as strategies and tactics used to ensure that a site is accessible to a search engines, which improves the chances that the site will be found by the search engine.
The goal of successful SEO is to obtain a high ranking placement in the organic search results of the search engines such as Google, Bing, Yahoo and others.
Higher website rankings means more traffic, more traffic means more costumers.
SEM stands for Search Engine Marketing and is a broader term than just SEO service.
SEM also contains the part of organic search optimization (SEO), but additionaly to this - SEM services also focus on helping you successfully target users of search engines via marketing, paid links in Google Adwords, Banner advertising or Facebook adverts etc.
SEO and SEM are not two competing services. SEO actually is considered as a part of SEM services.
SEM could be very useful when you start up a new website. Although your On-Page SEO is just fine and you are working on your Link Development, the search engines may not rank your website for your keywords, usually it takes from one month to six months or more, before your site is fully indexed, but even though your site is indexed - in may be ranked on page 3 in Google, Bing or Yahoo searches etc.
New website owners often call us in panic and say - "I can not find my side", or after a week - "even though I search for my keywords, I can not find my page "and so on. This is because the above problem, you need to have a lot of patience regarding the SEO, and indexing takes time.
So to help your business and website getting a good start, it may be useful in a period of 3-6 month to supplement your regular SEO, with SEM marketing, which could be targeted Google Adwords or semilar, then you will be visible in both the organic searches and in advertised links.