Registering tags taxonomy for a custom post type

The categories your code creates is a custom taxonomy, not the default post category taxonomy.

Anyway, if you want to add support for the default post tags taxonomy, the name is post_tag and can be added via the taxonomies argument in your $portfolio_args:

$portfolio_args = array(
    'taxonomies' => array( 'post_tag' ),
    // all of your other portfolio args
);

See register_post_type in Codex for more info.

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