To what extent the ancients understood the differences 
between flax, silk, cotton &c isn't particularly clear to me.

Mata, I can guarantee that the people who worked with flax, silk, cotton, wool, and byssus (and hemp, etc.) definitely knew the diffferences among them.  What we are undoubtedly dealing with, in a lot of the examples we've offered, is, well, just ignorance on the part of the author and/or a word that, early on, was misunderstood / misinterpreted and/or simple repetition of misinformation, etc.  It may sometimes be the classic case of the artist having no real clue what he (and it's usually a "he") is depicting when it comes to textile things.  We get this all the time in historical textiles.  I can name you quite a few medieval illuminations that show band looms that are mechanically impossible. 

 

Today, I came across an encyclopedia definition that defined "byssoid" as "cottony".  I threw up my hands in despair!

 

Nancy