I am having a hard time understanding what you’re trying to accomplish, but it’s probably just that I’m dense.
WordPress has theme files that live in /wp-content/themes/[theme name directory]/. One of them should be index.php, which is the default file used for everything, including posts and pages, unless there are other files in the theme directory.
If there’s a file in the the directory named “home.php”, then WordPress will use that (instead of index.php) as the template when someone requests your home page (by home page I mean the “Blog address” set under Options > General in the admin control panel).
Now it’s possible that you have created a page called “home” under pages in the WordPress admin control panel. (This has nothing to do with the home.php file; it’s just a name for a certain page that lives in the database, not in a file.) If you don’t have any other files in your WordPress theme’s directory, WordPress will use the index.php file when it shows the “home” page.
So, here’s what confuses me about what you’re saying. When we talk about a page named “home,” we’re talking about the content of a particular page created within WordPress, stored in the database. When we talk about the theme’s index.php file, we’re talking about a particular file used to markup that content, not the content itself, and it’s stored in a directory. They’re different kinds of things, just like the text in a book is different from a particular binding. So when you say,
I have a page called “home”. This page is different from index.php. I will like to make them the same page like in a standard html site.
I don’t understand what you mean.