Add custom tags for custom post type in WordPress

I have many custom post type and I want two of them to be relate by tags. These tags are only useable to these two custom post type only.

For example; I have two custom post type

1. books
2. writer

And I want these two post type have custom tag which only usable to these two post type.

How can I do that?

I try with Custom Taxonomies but didn't success.

this is a basic example i used you can change accordingly .

add_action( 'init', 'codex_book_init' );
/**
 * Register a book post type.
 *
 * @link http://codex.wordpress.org/Function_Reference/register_post_type
 */
function codex_book_init() {
    $labels = array(
        'name'               => _x( 'Books', 'post type general name', 'your-plugin-textdomain' ),
        'singular_name'      => _x( 'Book', 'post type singular name', 'your-plugin-textdomain' ),
        'menu_name'          => _x( 'Books', 'admin menu', 'your-plugin-textdomain' ),
        'name_admin_bar'     => _x( 'Book', 'add new on admin bar', 'your-plugin-textdomain' ),
        'add_new'            => _x( 'Add New', 'book', 'your-plugin-textdomain' ),
        'add_new_item'       => __( 'Add New Book', 'your-plugin-textdomain' ),
        'new_item'           => __( 'New Book', 'your-plugin-textdomain' ),
        'edit_item'          => __( 'Edit Book', 'your-plugin-textdomain' ),
        'view_item'          => __( 'View Book', 'your-plugin-textdomain' ),
        'all_items'          => __( 'All Books', 'your-plugin-textdomain' ),
        'search_items'       => __( 'Search Books', 'your-plugin-textdomain' ),
        'parent_item_colon'  => __( 'Parent Books:', 'your-plugin-textdomain' ),
        'not_found'          => __( 'No books found.', 'your-plugin-textdomain' ),
        'not_found_in_trash' => __( 'No books found in Trash.', 'your-plugin-textdomain' )
    );

    $args = array(
        'labels'             => $labels,
        'public'             => true,
        'publicly_queryable' => true,
        'show_ui'            => true,
        'show_in_menu'       => true,
        'query_var'          => true,
        'rewrite'            => array( 'slug' => 'book' ),
        'capability_type'    => 'post',
        'has_archive'        => true,
        'hierarchical'       => false,
        'menu_position'      => null,
        'supports'           => array( 'title', 'editor', 'author', 'thumbnail', 'excerpt', 'comments' )
    );

    register_post_type( 'book', $args );
}

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

// create two taxonomies, genres and writers for the post type "book"
function create_book_taxonomies() {
    // Add new taxonomy, make it hierarchical (like categories)
    $labels = array(
        'name'                       => _x( 'Categories', 'taxonomy general name' ),
        'singular_name'              => _x( 'Writer', 'Category singular name' ),
        'search_items'               => __( 'Search Category' ),
        'popular_items'              => __( 'Popular Category' ),
        'all_items'                  => __( 'All Writers' ),
        'parent_item'                => null,
        'parent_item_colon'          => null,
        'edit_item'                  => __( 'Edit Category' ),
        'update_item'                => __( 'Update Category' ),
        'add_new_item'               => __( 'Add New Category' ),
        'new_item_name'              => __( 'New Category Name' ),
        'separate_items_with_commas' => __( 'Separate Category with commas' ),
        'add_or_remove_items'        => __( 'Add or remove Category' ),
        'choose_from_most_used'      => __( 'Choose from the most used Category' ),
        'not_found'                  => __( 'No writers found.' ),
        'menu_name'                  => __( 'Category' ),
    );

    $args = array(
        'hierarchical'          => true,
        'labels'                => $labels,
        'show_ui'               => true,
        'show_admin_column'     => true,
        'update_count_callback' => '_update_post_term_count',
        'query_var'             => true,
        'rewrite'               => array( 'slug' => 'Category' ),
    );

    register_taxonomy( 'Category', 'book', $args );
    
    // Add new taxonomy, NOT hierarchical (like tags)
    $labels = array(
        'name'              => _x( 'Tags', 'taxonomy general name' ),
        'singular_name'     => _x( 'Tags', 'taxonomy singular name' ),
        'search_items'      => __( 'Search Genres' ),
        'all_items'         => __( 'All Tags' ),
        'parent_item'       => __( 'Parent Tags' ),
        'parent_item_colon' => __( 'Parent Tags:' ),
        'edit_item'         => __( 'Edit Tags' ),
        'update_item'       => __( 'Update Tags' ),
        'add_new_item'      => __( 'Add New Tags' ),
        'new_item_name'     => __( 'New Tags Name' ),
        'menu_name'         => __( 'Tags' ),
    );

    $args = array(
        'hierarchical'      => false,
        'labels'            => $labels,
        'show_ui'           => true,
        'show_admin_column' => true,
        'query_var'         => true,
        'rewrite'           => array( 'slug' => 'Tags' ),
    );

    register_taxonomy( 'Tags', array( 'book' ), $args );

    
}

for other post type you can use same code with change in post type and the taxonomy like

register_post_type( 'writer', $args );
register_taxonomy( 'Tags', array( 'writer' ), $args );