Category and post_tag are default WP taxonomies and since you attached them in your CPT functions so they appear in under your CPT and as well under Posts menu
What you need to do is to create a custom taxonomy lets call it movie_cat and attach to your custom CPT e.g. movies
// Register Custom Taxonomy
function custom_taxonomy() {
$labels = array(
'name' => _x( 'Movie Categories', 'Taxonomy General Name', 'twentythirteen' ),
'singular_name' => _x( 'Movie Category', 'Taxonomy Singular Name', 'twentythirteen' ),
'menu_name' => __( 'Movie Category', 'twentythirteen' ),
'all_items' => __( 'All Items', 'twentythirteen' ),
'parent_item' => __( 'Parent Item', 'twentythirteen' ),
'parent_item_colon' => __( 'Parent Item:', 'twentythirteen' ),
'new_item_name' => __( 'New Item Name', 'twentythirteen' ),
'add_new_item' => __( 'Add New Item', 'twentythirteen' ),
'edit_item' => __( 'Edit Item', 'twentythirteen' ),
'update_item' => __( 'Update Item', 'twentythirteen' ),
'view_item' => __( 'View Item', 'twentythirteen' ),
'separate_items_with_commas' => __( 'Separate items with commas', 'twentythirteen' ),
'add_or_remove_items' => __( 'Add or remove items', 'twentythirteen' ),
'choose_from_most_used' => __( 'Choose from the most used', 'twentythirteen' ),
'popular_items' => __( 'Popular Items', 'twentythirteen' ),
'search_items' => __( 'Search Items', 'twentythirteen' ),
'not_found' => __( 'Not Found', 'twentythirteen' ),
'no_terms' => __( 'No items', 'twentythirteen' ),
'items_list' => __( 'Items list', 'twentythirteen' ),
'items_list_navigation' => __( 'Items list navigation', 'twentythirteen' ),
);
$args = array(
'labels' => $labels,
'hierarchical' => true,
'public' => true,
'show_ui' => true,
'show_admin_column' => true,
'show_in_nav_menus' => true,
'show_tagcloud' => true,
);
register_taxonomy( 'movie_cat', array( 'movies' ), $args );
}
add_action( 'init', 'custom_taxonomy', 0 );
and the part where you are attaching custom taxonomies in your CPT function, use below code to attach movie_cat taxonomy
// This is where we add taxonomies to our CPT
'taxonomies' => array( 'movie_cat' ),