WordPress seems limited with the way it handles images (media). I don’t see why it can’t be part of the taxonomy like posts and pages since it is stored in the wp_posts table.
A media item is “attached” to a post if it has a value in the post_parent field. It can only be attached to one post.
If you have a gallery in a post and need to move them the only way to do it is via sql in the MySQL db.
Here is the sql to update in bulk media records to a new “parent.” You need the post ID for both the post you are moving from to the one you are moving to….
update wp_posts t1 set t1.post_parent = 713 where post_parent = 444 and post_type = ‘attachment’