This is the traditional view of Product Management from Pragmatic Marketing
Three domains are highlighted with circles: Strategic Management, Marketing and Technical Management.
Every function must exist on a Product organization
Each of these functions must have one or more R and a single A in terms of Responsibility assignment matrix
It has been my own view that I fall on the Technical Product
As PM is a leadership position within the Product organization, I would expect to be as C or I in all functions of the RACI matrix of the Product organization. In some instances, the definition and analysis of User Personas and Buyer Personas may also fall as R or A, on the shoulder of the PM.
The PO, which is a SCRUM construct, has a subset of the Tech PM. On many organizations, it is clear that PM should act as PO on the context of the development team practicing SCRUM. This subset of functions may be open for discussion, but I do not want to discuss that here.
However, some organizations, contract directly to the position of PO, which may indicate that the other tech functions are orphaned, or under the Strategic management. This may be the best configuration when you have multiple product layers; for instance: Content product, Front End product and API product (I experienced this many times at Elsevier, and yes I advocate that the API use of a product must have its own product team. I saw, also at Elsevier, a single functionality have its own Product Manager: the export function on Scopus (Yes, a manager for a button).
At a certain point in the Job
It would also be preferable, once this is cleared that the Informed and Consulted for each other function be discussed… most important of which is the Roadmap function.
It is important to note that these are the responsibilities from the POV of the Product organization. The SCRUM POV also has to be delivered by the PO. The overlap of responsibilities according to both POV’s is not a perfect match.