how to edit static "Home" page

Hi there. I’m in the process of developing my first WordPress theme.

I have a file which I named home.php, which I am hoping to use as the homepage (obvious one) that I can edit and style accordingly. I have gone into Settings > Reading section and made the “Home” page a static one. But how do I tie these two files together, so they’re styled differently than the internal pages?

Basically, I want the static homepage, where I can change the layout, add a slider, and so on, but for the internal static pages and even the blog I’ve set up, I want it to be styled differently. As of right now, my home and additional pages remain the same.

Please help!