How to transfer categories (default) to custom taxonomy?

wp links the posts and the terms in table wp_term_relationships so one doesn’t really have to worry about the custom taxonomy. You basically want to change the term ids from that of the default to the term_id of the new term in your custom taxonomy for your select set of posts. Lookup the term_ids and then do

UPDATE wp_term_relationships SET  term_taxonomy_id = 'newterm_id' 
WHERE term_taxonomy_id = 'oldterm_id' AND object_id IN 
(SELECT ID FROM wp_posts WHERE post_type="movies")