Clone a wordpress website with same functionality, but different content

Built in!

WordPress comes with feature for this: »MU« or Multisite or Network.

You can read more about it in Codex.

Summed up

The most important part is a single line in your wp-config.php file:

define( 'WP_ALLOW_MULTISITE', true );

Then you have to decide whether you want to use sub domains or sub directories.

One thing you’ve to be aware off: Not all plugins can be used in MU installations. Some have functionality, that depends on stuff like the $blog_id, which is a separate ID for every sub installation/clone/site you run. Always check this one first (Hint: Make one subsite that you use for testing).