I have not seen the term nonmalleable cast iron before, however I would comment as follows. Malleable irons are a distinct group of irons that come in several forms, black heart, white heart, bainitic, etc. this is a naming definition not a definition based on the property of malleability. Ductile iron is a name for spheroidal graphite cast iron. Again there are a variety of grades and types. Again this is a naming definition not a definition based on ductility. These two groups are totally separate, thus I would confidently say that ductile irons are not malleable irons. I would assume that irons that are not malleable irons are nonmalleable, this is based on naming conventions not on mechanical properties..
You can classify flake graphite iron and white iron as nonmalleable irons,though technically there is no such term as nonmalleable iron. It is a gift of the bureaucrats I suppose. I find such lose terms being used in India by the government agencies. Truly ductile iron is more malleable than malleable iron and malleable irons users and manufacturers are getting extinct
Generally malleability and ductility are similar concepts.
I think the primary difference between the terms malleable and ductile is in the type of alloy produced.
Malleable irons are intermediary between ductile and grey irons. They have intermediary physical characteristics (i.e. more ductile than grey irons but less ductility than true ductile irons) and intermediary microstructural characteristics.
They are physically made in different ways in different processes. Malleable or Ductile Iron is a definition of a "type" of iron.