please forgive me to answer to this thread so late, perhaps the issue has already been treated elsewhere on the forum. I just stumbled over the problem on my search for Feldmützen alter Art, as I want to try to make such an item.
Piping was usually (as long as the material was available) made out of Abzeichentuch, with a cord/rattan/metal ring etc. inside, or of the well known woven Gespinstlitze in silver or gold.
Later in the war prefabricated piping turned up. The problem with this was, that you couldn't join the ends by sewing them together - you had to join them by overlapping. There are pictures of caps somewhere in this forum which show that the overlapping was done in very different places on the cap - at the back seam of the crown or to the right or left of this seam. The piping of the cap band usually was not joined by overlapping at the back seam and certainly it was not simply sewn in at the back seam without overlapping. For me this always is a sign for a fake (please correct me if I'm wrong).
As to the pictures: on the cap there are different kinds of prefabricated woven pipings and for the cap itself I used such a piping, too (thus the overlapping). Then there are different ribbons and a Gespinstlitze which have to be sewn around an inlay (the above mentioned cord etc.) and a white self-made piping where this has already been done. This explains the plentitude of weaves and pipings - it all depended on what material one had and how it was produced.