Themes
A Theme is the overall design of a site and encompasses color, graphics, and text. A Theme is sometimes called a skin. WordPress site-owners have available a long list of Themes to choose from in deciding what to present to their sites’ viewers.
From the Appearance Themes Screen under the Manage Theme tab you can choose which Theme will be presented to users visiting your site. You can also view screenshots of each Theme you have uploaded to your site. In addition, under the Install Themes tab you can find and install new Themes.
Customize
The Customize Screen displays the settings that can be customized for a specific theme. This option will only be present if the Theme author has configured the theme to allow this capability. For instance, the WordPress Twenty Fifteen theme provides options that allows the user to set the colors and a background image.
The Customize Screen page describes the details of this feature.