Common differentiation of SEO is one on the basis of the legality of the techniques being used and on the basis of the location techniques are put to use.
On the basis of legality of techniques used SEO can be of two types:
Black hat SEO: The techniques that are considered as unethical and are therefore disapproved by the search engine.
White hat SEO: The technique which are considered as ethical and are thus approved by the search engine.
On the basis of the location SEO is practiced it can be either On-page or off-page SEO. As the name suggests, on-page SEO is one that is practiced on the webpage or website whereas off-page refers to one that is practiced beyond your website, generally on other websites and web pages.
Besides this there are many other types of SEO, which are rarely used, but are considered as a type of SEO.