While the content and format of organic search engine results varies depending on the search engine and the platform through which the service is being accessed (desktop, mobile, tablet, etc.), there is one definitive principle that defines an ad as native: native ads in search must present their content in a format and layout that is readily available to organic search engine results.
One common type of paid search ad will be found above the organic search results, look exactly like the surrounding results (with the exception of disclosure aspects), link to a page like the organic results, has been sold with a guaranteed placement so the agency knows exactly what context will surround it, and is measured on conversion metrics such as a purchase. This would fit into the IAB framework as follows:
Promoted listings are found on sites that typically do not have a traditional editorial content well, they are designed to fit seamlessly into the browsing experience, are presented to look identical to the products or services offered on a given site, link to a special brand/product page, are typically bought on auction directly via the publisher, are hyper-contextually targeted, and are measured on direct response metrics. This typical execution would fit into the IAB Native Framework as follows: