I only ever use private browsing mode. Firefox delete my history, cookies and cache every time I close my browser.
So unless Google have started to do browser fingerprinting, which I don't think they have, that shouldn't be the answer. At some level I believe that Google is just better at understanding my request, regardless of how poorly I formulated it, while DuckDuckGo just returns pages where some of the word match. Given that I don't know how any of the two search engines work I may be completely of.
Private browsing mode and deleting your local history doesn't stop Google from keeping its own log of your searches (and any other Google services (gmail, youtube), and pages with google-analytics, and any page with AdSense, etc)
Google clearly uses these logs to "customize" your search results, even when you check the placebo button to "disable" your history in the google account options.
Not having an account (or deleting local history) doesn't matter much, as they reconstruct a PK from all the entropy your browser leaks. (see their recent "we already ID your browser" reCAPTCHA update that no longer shows a scrambled image)
This isn't my experience, at least for YouTube. If I'm not logged into Google I only see "recommended for you" video links when I'm not in private browsing mode.
Harder to tell for Google Search - unlike YouTube I never see any indication that search results are based on my history, so any manipulation that's happening is opaque (I never search while logged in, so I don't know if the behavior is different in that case)
So unless Google have started to do browser fingerprinting, which I don't think they have, that shouldn't be the answer. At some level I believe that Google is just better at understanding my request, regardless of how poorly I formulated it, while DuckDuckGo just returns pages where some of the word match. Given that I don't know how any of the two search engines work I may be completely of.