A frequent topic of confusion among software development organizations is the proper role of a project manager as compared with that of a product manager.  Let’s start by defining the terms:

A product manager is responsible for the marketing strategy, direction and features of a product throughout its lifespan.  A project manager is responsible for the success and progress of a project on behalf of the project sponsor.  The confusion in part can be alleviated by confirming that project != product. A product by definition lives beyond individual versions; whereas in most organizations, a specific version of a product is a project.  This is articulated in more detail at How To Be a Good Product Manager:

Project managers are responsible for the successful delivery of a project — a one-time endeavor with a goal, scope, deadline, budget, and other constraints. A project manager will work to align resources, manage issues and risks, and basically coordinate all of the various elements necessary to complete the project. As they relate to products, projects can be undertaken to build a product, to add new features to a product, or create new versions or extensions of a product. When the project is complete, the project manager will usually move move to a new project, which may be related to a different product.

Product managers are responsible for the overall and ongoing success of a product. Once the project to build the product is complete and the project manager has moved on, the product manager remains to manage the product through the entire lifecycle. Other projects related to the product may be initiated, with the product manager being the one constant stream throughout, defining the project goals and guiding the team to accomplish the business objectives that have been defined.

As a product moves through its life cycle, changes are often conceived and added to the project roadmap.  The product manager, interested in delivering the very best product to the consumer, is an advocate of adding features that will make the product better or fix oversights regardless of the schedule.  The project manager, on the other hand, is interested in specifying an agreed-upon set of requirements and working towards their completion within budget and on schedule.  These interests are inherently in conflict.

The answer?  In my view, the project manager should be provided a list of stories or requirements for a release (or scrum) that are prioritized by the product manager, so that the project manager has the authority and the knowledge to add and remove stories/requirements as needed in order to come in close to deadline and budget–after all, everything will NOT go as planned, and not all of them will be done on time.  What isn’t handled in release 1 is simply held over or deferred for release 2.

In theory, over the course of several releases, as the product is able to meet more and more of the original set of requirements, that product has the chance to succeed in the marketplace.