Open the wish for editing and set a different destination wishlist. Saving moves it there.
Steps
Open the wishlist that currently has the wish.
Select the wish and open it for editing.
Change the wishlist the wish belongs to, picking your destination list.
Save. The wish now appears on the destination wishlist.
Good to know
You need Contributor access or higher on both lists, the one you're moving from and the one you're moving to. If you own both, you already have it. See "What is the difference between viewing and editing access?" in the Shared Wishlists collection.
There's no drag-and-drop between lists. Moving a wish is part of editing it.
Reordering is a different action. If you only want to change the order of wishes inside one wishlist, that's the move (reorder) action within that list, and it doesn't change which list a wish belongs to.
For other changes while you're in the edit form, see "How do I edit a wish?"