When using the WordPress search function results will display chronologically from newest to oldest. The search will look through posts, pages, categories, tags, titles, and content for matching terms.
The role of the URL when searching is to show users where they are within your site. The user can look at their address bar to see exactly where they have ended up on your site. The URL also tells search engines useful information about the page which helps to display your site when users are searching through other engines.
By using the >?php the_permalink(); ?< function, you can have your URL display the search term resulting in a more user-friendly URL.
WordPress search functionality is a great way for users to stay engaged on your site. It may require a little coding for URL and search.php for it to be stylized in a more appealing way.