But looking at https://en.wikipedia.org/wiki/Shades_of_pink it appears to lump your magenta (red/purple) into the same category as red/white. So really we've got 2 categories with the same name of 'pink'? 2 different things?
“Pink and magenta have the same hue. What distinction there is to be found between magenta and pink lies along other axes than that of hue [i.e. saturation and value]. All pinks are magenta and all magentas are purple, and by extension, pink is a purple. However, it does not work the other direction: it does not mean that all purples are magenta nor that all magentas are pink, let alone that all purples are pink.”
(Visit the link for a more detailed picture of the differences)