Return Taxonomy Name for Each Term

$term->taxonomy is the taxonomy name for each term, $term->term_taxonomy_id the – wait for it! – taxonomy ID.

To get the display names use get_taxonomy():

$terms = get_terms( array( 'category', 'post_tag' ) );

foreach ( $terms as $term )
{
    $tax_name = esc_html( get_taxonomy( $term->taxonomy )->labels->name );
    echo "$term->name ($tax_name)<br>";
}