I've spoken and written at length about what Product Design is in the past.
Product Design says "Yes, and," to all of what UX and UI roles do. This role can be a true unlock to business success when enabled and unleashed in the right direction with the right team to collaborate with.
Unfortunately, many organizations still struggle to get past the stigma and bias attached to the word "design" in Product Design, as well as imbuing the function with the qualities of other design functions they've worked with in the past, no matter how unrelated they may be or not. Seeing several folks try to visualize this, I came up with the following diagram tonight that I hope helps articulate things.
Necessarily, this diagram abridges quite a bit of information to get to the meat and potatoes of the matter (said the vegetarian, for some reason).
UI Designers are focused on visuals and production. They are output-focused in their role, generally taking orders from another function or leader, reacting to those to produce what they have been directed to produce.
UX Designers are generally focused on interaction design, accurate communication of information, information architecture (the hierarchical organization and arrangement of information), and, of course, usability. They typically do so in a highly collaborative fashion, working with a group of other functions, all focused together on measurable outcomes. A UX Designer, it's worth noting, is also generally focused solely on outcomes that benefit the end-user. The diagram is slightly unfair in that many UX Designers do research as well, but the trend as of late is that the more you add to a UI or UX designer's plate the more likely it is that they just become a Product Designer.
Product designers do all of these things, and more. A product designer also takes on many more areas of ideation, requirement gathering, testing, research, business logistics, and service design. A product Designer is also stretched to thinking not just about the end-user when chasing outcomes but also the business.
While a UI designer sits on one end of the spectrum, concretely knowing what they need to do and when they need to do it, because they take orders, UX and Product Design move further to the abstract end. Product Designers identify pain points and needs (business and customer opportunities), generating a lot of the work teams will chase.