The other kind, which is not discussed here, is where you have a web front end like startpage.com or duckduckgo.com which is making an API call to a search index in response to your query. In the US, the two english language indexes with decent precision and recall are provided by Google and Bing. One of Google's big partners there is Infospace which uses Google results in many of their properties. That said, when you use Google results in your search "engine" web page, you are bound by a different contract than the AdSense contract. And, like the AdSense contract, it is (or at least was) pretty restrictive on what sort of advertising you could do around Google's results.
 Bing either directly or through Yahoo!'s BOSS API if that is still a thing.