Why so many problems with labeling? Isn't that done in arts since ever? Don't people write "oil on canvas" or "oil on wood" if it is oil on canvas, or oil on wood? "Indian Ink drawing" or "charcoal slack" or "pencil"?
The Italian voice of Wikipedia describe seven different techniques of engraving:
I wouldn't be able to detect the difference observing the print, but technique certainly has an interest for those "in the know". And certainly ultimately it's the not the technique that determines the value. But it is not irrelevant information I believe.
Not a claim of superior quality. It's just a description of the technique used.