For very low voltage machines with a single conductor the wave winding has some advantage. For normal machines you need multiple conductors per slot and when you do that the length of wire becomes the same as a lap winding.
Groups of conductors per slot are just called coils and they can be lap or wave. Wave winding is more common with DC machines where the ends are linked by the commutator segments. With alternators and a wave winding you have to wind all the turns in by hand or you wind a skein and then wind that in and out of the slots.
Flux