Different categories for custom post type

Question

I use this code to create a new custom post type, but the problem is that it shows the same categories of default posts. Is it possible have different categories for this custom post type?

function crear_tipo_agencias() {
    $labels = array(
        'name'               => _x( 'Agencias', 'Post Type General Name', 'text_domain' ),
        'singular_name'      => _x( 'Agencia', 'Post Type Singular Name', 'text_domain' ),
        'menu_name'          => __( 'Agencias', 'text_domain' ),
        'parent_item_colon'  => __( 'Agencia Padre', 'text_domain' ),
        'all_items'          => __( 'Agencias', 'text_domain' ),
        'view_item'          => __( 'Ver Agencia', 'text_domain' ),
        'add_new_item'       => __( 'Añadir Agencia Nueva', 'text_domain' ),
        'add_new'            => __( 'Añadir', 'text_domain' ),
        'edit_item'          => __( 'Editar Agencia', 'text_domain' ),
        'update_item'        => __( 'Actualizar', 'text_domain' ),
        'search_items'       => __( 'Buscar Agencias', 'text_domain' ),
        'not_found'          => __( 'Agencias no encontradas', 'text_domain' ),
        'not_found_in_trash' => __( 'Agencias no encontradas en Papelera', 'text_domain' ),
    );    
    $rewrite = array(
        'slug'                => 'agencia',
        'with_front'          => true,
        'pages'               => true,
        'feeds'               => true,
    );    
    $args = array(
        'label'               => __( 'agencia', 'text_domain' ),
        'description'         => __( 'Agencias relacionadas', 'text_domain' ),
        'labels'              => $labels,
        'supports'            => array( 'title', 'editor', 'comments', 'thumbnail', 'custom-fields'),
        'taxonomies'          => array( 'category', 'post_tag' ),
        'hierarchical'        => false,
        'public'              => true,
        'show_ui'             => true,
        'show_in_menu'        => true,
        'show_in_nav_menus'   => true,
        'show_in_admin_bar'   => true,
        'menu_position'       => 5,
        'menu_icon'           => site_url().'/wp-content/themes/Avada/images/iconnoticias.png',
        'can_export'          => true,
        'has_archive'         => 'agencias',
        'exclude_from_search' => false,
        'query_var'           => 'agencias',
        'rewrite'             => $rewrite,
        'capability_type'     => 'post',
    );    
    register_post_type('agencias', $args);
}    
add_action('init', 'crear_tipo_agencias', 0);

Answer 1

You specify supported taxonomies right there:

'taxonomies'          => array( 'category', 'post_tag' ),

If you want different set you should configure it accordingly. Possibly registering custom taxonomies if that is what needed.