Both of these files go into the Theme directory. The index.php template file is very flexible. It can be used to include all references to the header, sidebar, footer, content, categories, archives, search, error, and any other page created in WordPress.
Or, it can be divided into modular template files, each one taking on part of the workload. If you do not provide other template files, WordPress may have default files or functions to perform their jobs. For example, if you do not provide a searchform.php template file, WordPress has a default function to display the search form.