A more definitive source for taxonomy of plants, especially in terms of genetic relationships (tribes) is:
Taxonomy Query for GRIN Species Records
Although it is not complete in terms of exotics and some plants only known in east Asia, it is constantly being updated. Credible suggestions are taken seriously. I recommend it to everyone.
The true Mulberries are in genus
Morus which is a group of species in the genetic tribe
Moreae.
As bananaT points out, the "Paper Mulberry" Broussonetia papyrifera is also in the genetic tribe
Moreae. The original classification in Morus was made in 1753 but updated by a taxonomist abbreviated "Vent." for which I have no reference. The plant is grown for fiber, not fruit. Here is an interesting article on the plant found in the references on the GRIN page:
Broussonetia papyrifera (paper mulberry). The plant is part of the germplasm collection at the
U.S. Natl. Germplasm Repository - Miami.
It would be unusual if any of the Morus species could pollenize a Broussonetia species, and stranger still for B. papyrifera since it is dioecious. If successful, the resulting seeds could grow interesting hybrids.