Product design is stepping into one's discomfort zone to do something different. Swimming against the current. Making a hard break.
Information architecture defines the structure of information (which can exist in many forms). Interaction design enables people to manipulate and contribute to/create that information. Visual design communicates these possibilities to people and creates affinity to them (desirability). Product design is the sum of these considerations.
Some might argue that the term 'information' is a bit limiting in this set of definitions and I kind of agree. So anyone who needs a broader purvey for what they work with could simply substitute 'information' with 'stuff'.
Product design for me is about combining intuition and empathy for solving customer problems with intelligence about what your team can build and market. We used to design products on a single team — our product team — at Moz. Now, we've moved to a format we call 'Adventure Teams' where folks from marketing, product, customer service, and engineering all come together to discuss things in an early kick-off phase. We define the problem people have, and we hear the user stories from our team members who've done customer interviews and our marketing team members who face this same challenge ourselves (we're lucky that we are our own customers). Then we define solutions that engineering can build, marketers can market, and customer service can support.
Product design isn't just about what a product looks like or does — it's about the interface between and experience of what an organization can produces to provide value to its consumers.
A Final Thought
Product Design is ever evolving and there are a diverse set of opinions on the matter. One thing is certain: the methods and principles of designing products, from prototyping to iteration, will endure.