Since you are a horse person, Tom, it might help to use the analogy of coat patterns in Paint Horses. To a casual observer, a horse with a tobiano coat pattern looks pretty much the same as one with an overo pattern. But, the genes that give rise to those two patterns are completely different and, I assume, an experience horseman can usually tell difference between them just by looking.
In a certain sense, irises can be split into two patterns: Plicatas and "regular" (for lack of a better word) irises. Plicatas are a recessive trait arising from a combination of genes. Ink Patterns is a classic example of the standard Plicata pattern, a light ground color with anthocyanin pigment around the edge of the petals. Usually the anthocyanin pigment has a speckled or stitched on appearance.
The Emma Cook pattern has some similarity in appearance to plicatas, light ground color with anthocyanin pigments around the edges of the petal (usually just the falls), but the genes that give rise to it are completely different. The Emma Cook pattern was developed from Amoena breeding, a "regular" iris pattern. If you look closely, the colored pigments on Emma Cook irises normally don't have that speckled appearance that is so typical of Plicatas.
The following pictures might help show the relationship between Amoenas and Emma Cooks.
Queen's Circle is a famous example of an Emma Cook
Amoenas have white standards and colored falls
Dancing Star had Queen's Circle (Emma Cook) as a pod parent and Starring (amoena) of the pollen parent. It's listed in the ATP as an Amoena, but you make the argument that it is an Emma Cook with a really broad band of color on the falls. I wonder which one Tom Johnson thinks it is, or if he even thinks about it at all?