Clicking on a link in a Google search results page creates a redirect URL that leads back to Google itself and logs the visit to your Google Web History if you are logged in. Its not a simple matter of referrals to third party websites. Its a personal detailed silo of personal information that Google sits on and can only stay private as long as Google can make good on its promise to.

DuckDuckGo, AFAIK doesn't log your searches or correlate your searches with a user account.