I have just looked it up on RHS ( Royal Horticultural Society) web site and it appears they are synonyms for the same plant. (RHS is the major UK plant authority, the Chelsea Flower Show is their most well known event)
and granatum and Nana&genus=Punica
In case the link doesn't work
"Punica granatum 'Nana' synonym of Punica granatum var. nana
Common name(s) dwarf pomegranate "