Product Managers define the ‘What and Why’ of the product- in consultation with customers, business leadership, marketing, sales/support, engineering (and other teams).
Project Managers define ‘When and How’ in consultation with product, engineering, QA and support teams.
For a project manager, product team is the customer.
What about success metrics?
Project Manager is often measured in terms of timely (bug-free) release.
For Product manager, the success metrics are a function of whether the release added value to the product or not (that is, tied to success metrics of the product).
Who owns critical decisions?
During development cycle, most of the crucial decision points are first spotted by Project Managers (Hey! We are gonna be delayed due to architectural flaw), but the actual decision is often taken by Product Manager (in consultation with senior management/marketing /sales and of course project management).
In many companies, product manager is often seen as a project manager who defines product requirements. Unfortunately, that’s one sad reality of the role but it is changing for good (Reality check: Many product managers also do project management part of the delivery including daily scrums/standups etc).