To move a wish to another wishlist, open the wish, edit it, and set the destination wishlist you want it to belong to. Saving moves it to that list.
Steps
Open the wishlist that currently has the wish.
Select the wish and open it for editing.
Change the wishlist the wish belongs to, choosing your destination list.
Save. The wish now appears on the destination wishlist.
Good to know
You need Contributor access or higher on both wishlists — the one you're moving from and the one you're moving to. If you own both lists, you already have this. See "What is the difference between viewing and editing access?" in the Shared Wishlists collection.
Moving to a different list is part of editing the wish, not a drag-and-drop between lists. Reordering is a separate action: if you only want to change the order of wishes inside the same wishlist, that's the "move" (reorder) action within that list, and it doesn't change which list a wish belongs to.
For other edits while you're in there, see "How do I edit a wish?"