A web browser is an app that uses a bar to direct the HTTP protocol commands to the server in order to display a page. A search engine on the other hand is a web page itself. It has an inbuilt access to data on the internet that it can pull to display all the relevant content.
Hence, a browser opens multiple web pages just like the one displaying the search engine. While the search engine is web page itself whose action is to search the entire web for relevant content. You can’t use the search engine to access websites. Not unless it directs you to a HTTP link that your browser identifies and opens.