A very common motif during the Byantine era is the Acheiropoieta (“made without hand”). Many things fall under this motif: Mandylion, Image of Edessa, Veil of Veronica, Our Lady of Guadalupe, and the Manoppello Image.
Acheiropoieta (Medieval Greek: αχειροποίητα, “made without hand”; singular acheiropoieton) — also called icons made without hands (and variants) — are Christian icons which are said to have come into existence miraculously; not created by a human. Invariably these are images of Jesus or the Virgin Mary. The most notable examples that are credited by tradition among the faithful are, in the Eastern church, the Mandylion, also known as the Image of Edessa, and the Hodegetria, and several Russian icons, and in the West the Shroud of Turin, Veil of Veronica, Our Lady of Guadalupe, and the Manoppello Image.
Icons created by divine agency were known as acheiropoieta (“not made by (human) hands”). This category of miraculously created image was accorded special veneration throughout the history of Byzantium. A significant number of acheiropoieta originated in the Early Byzantine period, before the advent of Iconoclasm in the early eighth century.
This motif started in the 6th century.
The belief in such images became prominent only in the 6th century, by the end of which both the Mandylion and the Image of Camuliana were well known.
If the TS is legit, then it is reasonable the shroud is the archetype of all the Acheiropoieta images. All Acheiropoieta icons were then either referring to the TS itself or to copies inspired by the TS.
The term is also used of icons that are only regarded as normal human copies of a miraculously created original archetype.
There is no surviving relic that can be claimed to be the original archetype other than the TS. The TS is the sole artifact that is in our possession that can be scientifically tested to be not made by human hands. Even to this day, we have no idea how to fully replicate it. And since all the copies were made by human hands, I think it makes more sense the term Acheiropoieta applies not to the copies, but to the original archetype that all of them is based on.
Video explaining Acheiropoieta: