Different slug taxonomy for two different CPT

You can share a taxonomy between multiple custom post types.

You will need to register the taxonomy in your plugin file or theme’s functions.php file:

<?php register_taxonomy( $taxonomy, $object_type, $args ); ?>

WP Codex: Registering Taxonomies

When you register your taxonomy you will need to use an array for the $object_type. In this example the taxonomy “city” is being assigned to the “people” and “cars” post types:

register_taxonomy(
  'city',
  array( 'people','cars' ),
  array( 'hierarchical' => true,
         'label' => __('City'),
         'query_var' => 'city',
         'rewrite' => array( 'slug' => 'city' )
  )