Creating slightly different sites using same code base
The standard way of doing this is called a &quot;multi-site&quot;.  It allows you to use the same codebase for multiple sites.  Each site in a multi-site has its own settings.php, so you may use different databases or the same database (this is controlled by the database settings in settings.php.
To use a different logo, just  go to appearance &gt; settings and upload a different image for the logo.
Here is a link to my tutorial about setting up a multi-site:
http://wikihandbooks.com/drupal7/intro_multisite.html
There is also instructions at Drupal.org: https://www.drupal.org/docs/7/multisite/multi-site-sharing-the-same-code-base