Both use keyword research to uncover popular search terms. The first step for both SEM and SEO is performing keyword research to identify the best keywords to target. The research includes looking at keyword popularity to determine the top keywords or buying keywords that your ideal audience searches for. It also includes looking at keyword competition to see what other brands are targeting the same keywords and determining what you will need to do to compete with those other companies.
The key distinction is that SEM is a broader strategy which combines paid search and SEO tactics. So, if you set up a PPC advertisement, but don't take steps to optimize the ad or the website it links to, this is a standard example of paid search. However, if you optimize your site and your search content with solid keywords, then you put money behind it to boost it on targeted audience's search pages, then you're dabbling in SEM.