Sometimes the names can be misleading as home.php actually refers to the page that stores all of your blog posts.
In general, use either page-home.php or front-page.php for the home page and then page.php for the rest. Whenever you have a specific page with a different layout, you can create a new template that is styled specifically for that. Eg. page-contact for a contact page that doesn’t follow the styles of other pages. The page-XXXXX.php is dependent on the slug of the page so that is how WordPress finds it.