Safari is a Browser. "DuckDuckGo Private Browser" is also a browser.
"DuckDuckGo" is a search engine that provides the same functions as Google without all the advertising and trackers. The developers behind DuckDuckGo built search functions into most browsers to allow you to set DDG as the default search engine. Then they developed browser extensions to automatically set the search function to DDG and also add some privacy enhancing features. Then they developed their own browser as a privacy focused alternative to mainstream browsers.
Regardless of that...for you, the important question is - what browser are you actually using? The Apple default is Safari. Unless you installed another browser on purpose (including DuckDuckGo Private Broswer) and changed your default browser, then you use Safari.
If you did change the default, then launch Safari. Go to the Safari Menu, specifically Safari>Preferences. The first pane is general preferences, and the very first thing on that page should be the confirmation that Safari is your default, and if it isn't, there will be a button to set Safari as default. There is another pane for search preferences, which is where you could/may have set DDG as the default search engine.