Share Tags Between Custom Posts in Admin

When you register_taxonomy you can simply add an array of post_types to $object_type parameter.

From WordPress-codex:

(array/string) (required) Name of the object type for the taxonomy
object. Object-types can be built-in objects (see below) or any custom
post type that may be registered.

So you can just add an array of post_types after you run register_taxonomy and its name in this case “genre”.
See code below:

//hook into the init action and call create_book_taxonomies when it fires
add_action( 'init', 'create_book_taxonomies', 0 );

//create genres for the post_types post and page
function create_book_taxonomies() {

  $labels = array(
    'name' => _x( 'Genres', 'taxonomy general name' ),
    'singular_name' => _x( 'Genre', 'taxonomy singular name' ),
    'search_items' =>  __( 'Search Genres' ),
    'all_items' => __( 'All Genres' ),
    'parent_item' => __( 'Parent Genre' ),
    'parent_item_colon' => __( 'Parent Genre:' ),
    'edit_item' => __( 'Edit Genre' ), 
    'update_item' => __( 'Update Genre' ),
    'add_new_item' => __( 'Add New Genre' ),
    'new_item_name' => __( 'New Genre Name' ),
    'menu_name' => __( 'Genre' ),
  );    

  register_taxonomy(
    'genre',
    array('post', 'page'), // add your post_types here
    array(
        'hierarchical' => false,
        'labels' => $labels,
        'show_ui' => true,
        'show_admin_column' => true,
        'query_var' => true,
        'rewrite' => array( 'slug' => 'genre' ),
  ));
}

Then you share the same data on dose post_types.