Categories and tags for custom post types

Question

I'm having a hard time explaining this, so bare with me.

Category and tag links for my custom post type aren't working as I expected them to. Instead of getting http://www.example.com/projects/category/example-category, the links that are http://www.example.com/category/example-category. In other words, I can't figure out how to make my categories post-type specific. In the dashboard, my Projects post type has both a Tags and a Categories section, but editing them results in the same changes being made to the main Posts post type.

How can I create post-type specific categories?

Here's my code to create the post type:

function projects_create_post_type() {
    $labels = array(
        "add_new" => "Add New",
        "add_new_item" => "Add New",
        "all_items" => "All Projets",
        "edit_item" => "Edit",
        "menu_name" => "Projects",
        "name" => "Projects",
        "new_item" => "New",
        "not_found" =>  "No projects found",
        "not_found_in_trash" => "No projects found in Trash",
        "search_items" => "Search Projects",
        "singular_name" => "Project",
        "view_item" => "View",
    );
    $args = array(
        "has_archive" => true,
        "hierarchical" => false,
        "labels" => $labels,
        "menu_icon" => __("dashicons-hammer"),
        "menu_position" => 5,
        "public" => true,
        "slug" => "projects",
        "supports" => array(
            "editor",
            "thumbnail",
            "title",
        ),
        "taxonomies" => array("post_tag", "category"),
    );
    register_post_type("projects", $args);
}
add_action("init", "projects_create_post_type");

Answer 1

You need to create taxonomies specific to your post type using register_taxonomy instead of using the taxonomies argument when registering the post type.

http://codex.wordpress.org/Function_Reference/register_taxonomy

// categories
register_taxonomy(
  'project_categories',
  'projects',
  array(
    'label'        => __( 'Categories' ),
    'rewrite'      => false,
    'hierarchical' => true,
    'capabilities' => array( 'edit_terms' => 'manage_categories' )
  )
);

// tags
register_taxonomy(
  'project_tags',
  'projects',
  array(
    'label'        => __( 'Tags' ),
    'rewrite'      => false,
    'hierarchical' => false,
    'capabilities' => array( 'edit_terms' => 'manage_categories' )
  )
);

Answer 2

If you need to output tags for custom post type - here good example https://jamper.online/vyvod-tegov-tags-dlya-kastomnyh-postov-custom-post-type

    function get_terms_by_custom_post_type( $post_type, $taxonomy ){
    $args = array( 'post_type' => $post_type);
    $loop = new WP_Query( $args );
    $postids = array();
    // build an array of post IDs
    while ( $loop->have_posts() ) : $loop->the_post();
        array_push($postids, get_the_ID());
    endwhile;
    // get taxonomy values based on array of IDs
    $taxonomies = wp_get_object_terms( $postids,  $taxonomy );
    wp_reset_postdata();
    return $taxonomies;
}