How to use different CSS for home page and inside page?

There are a lot of options for doing what you want. First, take a look at the source code that your theme generates. You may find that it adds a special class to the body tag for the front page. If it does, you can use this class to define css rules that apply only to the front page.

See this page: http://drupal.org/node/225868 for instructions on how to add a CSS file to your front page (or any other page).

Another option is to use the Sections module which permits you to apply a different theme to a particular section of your site.