Great writing but I also do not seem this information provided is reliable.

User Experience designers is a role which does incorporates intersection about user, technology and business. Both work for crafting a better experience eventually. But product designers is responsible in flaws of result in user experience and consider a product as a whole to attain the goal and build strategy on it.

The responsibilities written is totally can be overlapped. Most of the product designer role is also suitable for UX'ers. Simply UX deals directly with users but PD deals with overall product and artifacts associated with it.

Still there are lot of controvercies matters found online about this topic which may be misleading.

Also thankyou for writing this.