According to the PMI (Project Management Institute) the product scope is what the product should or should not be, or do, once completed.
For example the scope of a new coffee machine to be manufactured could be to make not only espresso coffee but also cappuccino and hot water for tea.
The Project scope are the activities and deliverables that need to be performed / delivered during the project life cycle.
For example, customer training on the product could be part of the project scope but is definitely not part of the product scope.
In terms of project evaluation, the product scope is to be measured against the product requirements, while the project scope should be measured against the project plan.