Search indexes have a reasonably unique fingerprint in the rank order of organic results for a given query. The ads and sponsored content are all over the map and perturbed by a/b tests and other things but the organic results typically come straight from the ranking algorithm.
Most "Search portals" (which is the web page that you type at to get your search engine result page from (SERP)) are either using one of the two English language indexes (Bing and Google) with their own ad network, or "blended" index where the search portal might index somethings like Wikipedia and Stack Overflow and then use Bing or Google for the long tail stuff.
The reason for this is economics, you can stand up a search portal on an AWS instance, feed all the queries to Bing out the back and sell ads on it and make a few bucks.
In contrast building your own index requires many more servers, crawling over the content you want to index (if you want to keep it fresh) and generally much larger network and storage costs. So its harder to pay for that with third party ad networks (not impossible, just harder). Pretty much everyone skips this approach for that reason.