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The Project Scope includes all the work needed to be done to create a product, or deliver a service, or result. The Project Scope is all about the project, it defines the requirements of products, the work required to create the product, and defines what is in the scope and what not.
The Product Scope is the characteristics, features, or function of the product, service, or result. It is the outcome of the project. The Product Scope is all about the product: how will it look like, how will it function, etc.
product scope is the requirements that relate to the product of the projectis and the project scope is the work the project will do to deliver the product scope or product of the project
Product scope only refers to what is needed to get this product (i.e. technical specs, technologies, features, etc...), while project scope handles the roadmap to create the product/service/output.
Project scope relates with the deliverables and the product scope relates with the functionalities of product.
A product can have multiple projects in it. so a product statement will tell you about the needs of product and main projects being involved to complete this product. What are the needs of this product.
While project scope statement is related to that project alone. what part of the product will it complete why is it needed and what needs to be done to complete the project etc.
Wrt PMBOK (According to5th Edition)
Product Scope: Features and Functions that characterize the product, service or result
Project Scope: Work to be performed to deliver the product, result with specified features and contents
I thought this would be the most simplest way to answer it!