Product Management and Project Management are sometimes used interchangeably.
Some People even think they are the same.
The 2 fields have Intersections but they are not the same.
According to the Project Management Institute (PMI);
a project is a temporary endeavor undertaken to create a unique product, service or result.
Projects are temporary with a Start date, an End date and definite Goals.
Hence, Project Managers handle Projects, deliver and move to the next One.
Product Management on the other hand is continuous throughout the lifetime of a Product.
Product management is the business process of planning, developing, launching, and managing a product or service.
While a Product might be a Project at the onset which will require Project Managers overtime it becomes a continuum which will require an actual Product Manager.
Think of it like a Child.
There is a 9 Months Project of birthing a Child after which Parenting (Product Management) goes on throughout the lifetime of the Child.
I wish You the very best.

I am Seun Ogunmola I help People and Organizations to leverage on Technology to achieve their goals Faster, Easier and Cheaper.
I also write on diverse subject areas including Finance, Business, Productivity and Governance.