A browser and a search engine are not the same thing
Chrome, Firefox, Edge and Safari are browser programs. Google, Bing and DuckDuckGo, on the other hand, are search engines used within a browser. The two are often confused in everyday conversation. For technical questions, however, it is almost always the browser and its exact version number that matter.
Good news for you: the provider and version are identified as soon as you open this page. You do not need to install a program or search for hidden settings.
Why knowing the exact version matters
Two users can have the same browser and still see different results on a website. Often this is simply due to an older browser version. New browser versions close security gaps, fix errors and support current web technologies.
BrowserDetails.org compares the detected version with the latest published vendor data. If an update is only just starting to roll out gradually, this is taken into account separately. This avoids an immediate warning just because the new release is not yet being offered on every device.