Thanks Baja! I read the entry incorrectly. Was still drinking a.m. coffee. Should have waited to respond and read original post again.
I'd think Mammillaria would be a common name for a lot of cactus. Sort of like the use of Opuntia. More of a family apellation than a name specific to a cultivar. That's what I call several I'm growing because they arrived unlabeled and my best guess is Mammillaria. So I call them Mammillaria. Not helpful except in a general way.