They wanted to know what the difference between a "cap" hair net and a "fringe" hair net.
Now, I had never heard of either until that post. On the quest for correct information, I did my research. And by research I typed in "cap fringe hair net" in google.
Found a link to this book (available for free on google books!), published in 1940: Accessories of Dress: An Illustrated Encyclopedia .
Here's the blurb with the answer:
"The business of making hair nets began to decline in 1923. This was due to the popular fashion of bobbed hair. When this fashion swept the country it forced forty thousand girls in Shanghai out of employment. This decline in business continued until 1929, when a modified return to long hair increased the demand for nets. By this time, however, a small, cap-shaped net for bobbed hair had entered the field and attained great popularity. Milady of fashion could now call for a 'cap' net, or, if she preferred, the 'fringe', which was made for long hair."
So the answer, in short, "cap" hair nets are for bobbed hair; "fringe" hair nets are for longer hair.