Marty Cagan argues that splitting the Product Manager and Product Ownership roles into two positions is a mistake:

This approach has two common negative consequences.  The first is that there is no clear owner (neither person takes responsibility for the product), and the second is a common lack of respect or understanding between the two (the “product manager” doesn’t appreciate the technical complexities, and the “product owner” doesn’t appreciate the customer’s pain).

I agree, and I would actually go one step further. I view Product Ownership activities (representing the voice of the customer, interacting with the development team, managing the backlog, etc.) as a subset of the overall strategic Product Management position (product planning, execution, and marketing). I’ve resisted calling my team Product Owners, and prefer to say that they are Product Managers who fulfill a Product Ownership role on Agile projects.

The problem is that splitting these roles into distinct job titles also splits their goals. It’s easy for one to become all about the market, and the other to become all about internal development tasks. Instead, a Product Manager should ultimately take end-to-end responsibility for the development of product solutions that meet user goals and business needs. That’s the job. Managing the backlog and working with developers on specifications are just part of that overall function, not a thing on its own.