On other search engines, they all rely somewhat on either Google's or Bing's web crawling: Qwant, Bing and Brave, Google (and Bing for images). This is easy to see as a webmaster since you don't see their crawlers much (if at all). Only Google and Bing are doing full scale web crawls. However, search is a lot more than traditional web links -- in fact it is about half now from instant answers that can come from dozens of sources and indexes (which the above comment gets into).