How to create a category or tag available exclusively to the admins and not to the users?

Sure, you can restrict access to a tag with the following code:

add_action('save_post', 'remove_tags_function', 10, 2); 
function remove_tags_function( $post_id ){
    if(!current_user_can('manage_options')){ 
        $post_tags = wp_get_post_terms( $post_id, 'post_tag', array( 'fields'=>'names' ) );
        $pos = array_search( 'ExclusiveContent', $post_tags );
        if( false !== $pos ) {
            unset( $post_tags[$pos] );
            wp_set_post_terms ($post_id, $post_tags, 'post_tag');
        }
    }
}

So, with this code, whenever a normal user adds the tag ExclusiveContent, it will be removed upon save unless if the current user can manage_options. This code should be added to your functions.php file. You can find this file in your theme’s folder.