In Project Management context, clarification on Product Scope and Project Scope is important & it helps easy management of the project.
Project is the one which is executed to create a unique product or services; and
Product is the outcome of a Project.
With above definition in mind let us review their scope definition:
Product scope: The features and functions that characterize a product, service, or result
Project scope: The work that needs to be accomplished to deliver a product, service, or result with the specified features and functions. 
Product scope can remain constant at the same time that project scope expands which is called as Progressive elaboration. Progressive elaboration should not be confused with scope creep. Progressive elaboration is giving more details for the already defined scope and not increasing the project scope. And
Scope creep is adding features and functionality (project scope) without addressing the effects on time, costs, and resources, or without customer approval.
My building contractor estimated the work on my house construction. He thought that he will be using special type of cement for concreting. But that special cement was not available in our place. He explained me who was responsible for ordering and delivering the materials from his side. Taking on that responsibility doesn’t change the product scope (house construction), but now the activity (in project scope) & its responsibility was completely explained. (Progressive elaboration)
After contractor started the work with the plan & estimate, my wife suggested me to add a wall construction near the entrance. But this was different from what we agreed. So, contractor told me this was an extra work and he did it with extra money. (Scope creep)
. PMBOK® Guide – 3rd edition