It sounds as if you're getting "browser" confused with "search engine". Safari is a browser, an app that allows you to access the web. Other browsers include Firefox, Chrome (by the makers of Google), Brave and many others. "Google" (in this context at least) is a search engine, a site you navigate to using a browser and input a search query.
You can choose your default search engine by going to Settings>Safari>Search Engine. There is no "Safari" search engine. Apple does not have its own search site.
Safari is the default browser unless you change it. If you download another browser, such as Chrome, you can go to Settings>Chrome>Default Browser App and select something different. If you do that, you will then see Settings>Safari>Default Browser App. But, if you don't choose a different browser as default, you won't see that setting. In other words, if you don't see that setting, Safari is the default browser.