Kagi is a Meta Search engine (it uses other search engines API e.g. Google, Yandex, Brave Search, Marginalia, ...) + it has its own (tiny) index, their own index mostly consits of their "Small Web" pages.
>Our own index of the finest results augmented by the results from the best search engines on the market.
DDG uses Bing. Them blocking trackers except when they come from Microsoft (because of this search engine deal) is why I don't really care about using DDG.
You can use bangs to search on Google, but that's not the default.