If you move a topic from A to B that the user already read, there won’t be any notification.
If you move a topic from A to B the user didn’t read, there will be, in some cases, an edit notification. In others, a new topic notification.
It may send an edit notification when the topic is partially read, and a new topic notification when we didn’t read it at all.
Moving a partially read topic with unread replies (edit notification):
Moving first a read topic (no notification), then an unread topic (new topic notification):