I'm not sure if this is still a grey area, like something not totally defined, we have books about user interface, interaction, user experience, but I haven't seen any book about digital product design.
Not trying to be a jerk, but isn't digital product design encapsulated within "user interface, interaction and user experience"?
Check out A Book Apart http://www.abookapart.com/ I found 'Designing for emotion' to be an excellent read.
I'd argue that 'digital product design' encapsulates all those, but extends to include things like customer experience
UX was intended to be a bit holistic in nature, but is still primarily concerned with user interfaces./users of a product It is more holistic in that it's not only concerned with performance/usability (HCI/Human Factors), but feelings and other apparent 'intangibles'
Customer Experience is the customer of a company's whole experience with their product, including things that aren't limited to a user interface.
Digital product design, is designing something as a PRODUCT. So not just doing the interaction or UX of a product, but examining the product/market fit, or design from a holistic level (not just high level or low level)
For what it's worth, I'm not really a fan of the proliferation of such terms, especially when they are used indiscriminately.
A great book which I highly recommend is "Designed for Use" - Create Usable Interfaces for Applications and the Web by Lukas Mathis
It goes through all steps of product design. The structure of the book is great to start reading from the beginning or somewhere in the middle. At the end of each chapter there is a nice wrap-up with take aways.
Check out, Inspired: How To Create Products Customers Love by Marty Cagan. It's targeted towards Product Managers, but he takes a lot of design principles on developing products to apply it to product management. http://www.amazon.com/Inspired-Create-Products-Customers-Love/dp/0981690408
A product designer, at least in the capacity that I've been a product designer, has to balance product goals and user goals, design the ux and ui. So Victor M. defines it well in his comment.