Very slow update with subquery (different tables)
The subquery will be executed for each row from the outer query, and no index will be used. In addition, 0.6 sec is "relatively" long. For example, if you have 1000 rows in domain table, then expect more them 600 sec (10 minutes).

In the second query, MySQL is able to use the index on 'domain'. This is a feature of using "IN" instead of subquery.