Search Engine Marketing, or SEM, is the umbrella term for any form of marketing done via search engines. Two of the branches of SEM are search engine optimization (SEO) and Pay Per Click (PPC) advertising.
The results that search engines return can be classified in two ways: organic results, which are the links (now interspersed with news, maps, images, knowledge graph answers, etc.) that the search engine algorithm determined to be the most relevant to a query, and paid results, which occupy the space along the perimeter of the organic results shaded in a different color that are auctioned to advertisers.
SEO is the process of improving a website’s traffic from the organic results while PPC advertising is the process of improving a website’s traffic from the paid results. PPC can also refer to banner advertising on other websites as well, but SEM is not a synonym for PPC despite being a commonly held belief (blame Yahoo).
There is also an often-misunderstood distinction that SEO is “free”. Unlike PPC advertising, which requires continued spending to keep your ads appearing, SEO requires no direct payment (neither one time nor recurring) to search engines. SEO is, however, massively hard to duplicate for latecomers, expensive to execute (just buying links or tricking the algorithm violates search engine guidelines), and requires tremendous creativity paired with technical skill and a time-bounded network effect.