Yes. All Norway/Fancy/Dumbo/Rex/Hairless/etc etc are of the species Rattus norvegicus.
I'm not very knowledgeable about ASFs. But like what Redneck_Crow said, they're a different species as Norways. They're of the species Praomys natalensis. I believe ASFs are more commonly known as Natal Rats to the pet community. But I could be wrong.