Custom WordPress the_terms() function to sort the post terms by "Category Order and Taxonomy Terms Order".

functions.php

<?php

/**
 * The terms
 */
function prefix_the_terms( $post_id, $taxonomy ) {
	$term_ids = wp_get_post_terms( $post_id, $taxonomy, array(
		'fields'  => 'ids',
	) );

	$terms = get_terms( $taxonomy, array(
		'include'    => $term_ids,
		'orderby'    => 'term_order',
		'order'      => 'ASC',
		'hide_empty' => false
	) );

	$links = array();

	foreach ( $terms as $term ) {
		$link =  $link = get_term_link( $term, $taxonomy );

		$links[] = sprintf(
			'<a href="%s" rel="tag">%s</a>',
			esc_attr( $link ),
			esc_html( $term->name )
		);
	}

	echo implode( ', ', $links );
}