Product Management:

Involves vetting the development and lifecycle of a product
Defines the features and requirements of the product
Works with a cross-functional team to build and design the product
Manages the product's roadmap and launch
Ensures that the product meets the needs of the target market and is successful in the marketplace

Project Management:

Involves planning, organizing, and managing resources to complete project goals and objectives
Defines the project scope
Establishes a project plan
Ensures the project is completed within budget and on schedule