Custom taxonomy- only output relevant terms

You can use another argument in the array of argument, you have many choice to filter the results.

You can add exclude, include with an array or comma separated of the terms you want to display.

$terms = get_terms( array(
            'taxonomy' => 'product_provider',
            'include'=> array('X', 'Y')
);

But, if the results depends on the product_type, you’ll maybe need to use meta_key and meta_value (of the product).

Of course you can mix, all these arguments if need.

If you want to get the term that belong to a product, you need to use wp_get_object_terms().

You will find all details get_terms and wp_get_object_terms

Hope it helps.