There are only 2 ways how you can market your website on search engines.

1. Organic Results
2. Paid Advertisements

Organic results are often referred to as search engine optimization. Search engine optimization or SEO as it is popularly known is the process of optimizing a web page in such a way that it achieves higher organic rankings (no payment is required to the search engines) for its primary keywords across search engines.

Paid advertisements is a process in which the search engines will place your company's advertisement (text or banner depending on the channel selected) on their website or their partner sites.

Definition wise all the marketing done on search engines is referred as search engine marketing (SEM), so SEO is also a part of SEM.