Well, the clue is in their names. Project managers manage projects, which could be anything. They juggle resources and timelines.

Product managers are responsible for the direction of a product. They have to figure out what customers want or need and ensure that the product being built satisfies some of those needs and is competitive in the market place.

There may be some project management in product management, but there is no product management in project management.

Project Managers oversee the building of new stuff.

... then Product Managers move in and squat.