Here's a brief backgrounder on the nomenclature, for what it's worth.
Thanks for the link.
I may be wrong, but my take on it is that the product most used in food preparations, and medicines are pyridoxine.
That’s not to say that there aren’t any other forms of B6 available in the retail or hospital pharmacies. New items are coming along all the time.
Still, I have spent 35 years in pharmacy, and the vast majority of vitamin B6 used there, in tablet and injectable forms, have been referred to as pyridoxine.