Also good to note that titles and roles depend on the company.
A Project Manager at Company X might also be the Product Manager and vice-versa.
I like to think of the Product Manager as the Product Owner. He/she has the industry experience and target audience knowledge and is the driving force behind defining the product.
1. Project manager: make sure the product (as defined by someone else) ships on schedule with the top priority features (as defined by someone else).
2. Product manager: make sure the product meets user needs. This may involve some project management as well.