Clearly, there is a discrepancy here. The original Edessa story recounts an image of Christ made by Christ prior to His crucifixion. Meanwhile, the Holy Shroud of Turin is a full body image of a crucified and resurrected Christ. So then, there are either two images (pre-crucifixion face-mandylion, and the post-crucifixion body-shroud of Turin), or just one image and thus the ancient origin narrative of Edessa about Saint Jude is false. Or maybe Saint Jude did bring an image of Christ to Edessa (the Shroud of Turin) and the story about Christ wiping His face on fabric is the only incorrect part of the original story. (Is the Veronica story being confused here in this ancient legend? Who knows?)
I, personally, don’t know how to untangle the accounts. It seems pretty clear to me that what is being called the "Image of Edessa" in AD 944 is the Shroud of Turin since the Edessa Image here is a full body image. It also appears that there is a strong tradition for this image being transported to Edessa through the hands of Saint Jude Thaddeus.