The Turin shroud is a medieval fraud, proven by carbon dating and two different researchers working independently (Dr. Nicholas Allen in Africa and Picknett and Prince in the UK) proving it likely to be an image created by heated linen soaked in light sensitive chemicals and a Camera Obscura.
Stigmata are a mix of some frauds perpetrated by religious maniacs self harming(or more disturbingly harming their children), and a seemingly not fully understood syndrome causing lesions in the hands and feet, that though assumed to be religious in nature are not consistent with actual damage done by crucifixion where the wounds were in the wrists and ankles.

The Churches, the Catholic Church in particular, have been pulling all kinds of scams on people for centuries, scams like Holy Relics being the finger bone of some Saint for example, to get the fear-filled, poor believers to go on more and more pilgrimages, etc, and give more and more money to the church/churches.
For example, when I was a High School Student back in the mid to late 60s we had a Catholic Priest show us his crucifix that he claimed was hand carved from a piece of the Holy Cross, one simply look at it told us that it was indeed hand-carved BUT carved from Australian Eucalyptus ( Gum Tree), a tree that never ever grew in the Middle East.
It is a very simple thing, though 1,000% immoral and utterly ghoulish in my opinion, for any religious organisation to actual dig up a long dead body, remove a bone/skull, etc, place it in a nice fancy case and CLAIM it to be a Holy Relic of some long dead Saint, etc.
As for the Shroud, well science has proven that it is a FAKE, a 100% fake and most like a result of an experiment done by Da Vinci or another scientist of that period.
Stigmata are simply occurrences that can occur as results of diseases within the body exhibiting themselves on the skin, etc, and are simply falsely claimed by religions as being holy signs, etc.

I will be waiting, breathless, for your comments.

No, it's the side making extravagant claims that needs to provide evidence.

I once had severe eczema that resulted in bleeding sores on my hands and feet. Now, if only I had gotten a similar sore on my side, I could have claimed stigmata.

As for the Shroud of Turin, it has been shown to have been a later forgery.

[history.com]

[livescience.com]