If youre even a bit familiar with the WordPress themes, by now youve probably took a look at your themes files. Blog pages are rendered through an association of a few PHP files with standard names (index.php, archive.php, single.php) with different templates of the theme, based on the content type.
The index.php file usually stands for your home page, also being capable of replacing any other template that hasnt been already defined. So, if you dont have a template for search results (search.php), the index file will take over and render your search results page.