A new employee in the accounting department is having difficulty understanding two sets of ...

First, you should explain that all costs should be first classified as either variable or fixed. This concept deals with cost behaviour and not with what the costs are associated in the organization. Many decisions are made about costs because of the type of behaviour they exhibit.
Second, a cost can be assigned to "why you are in business" activities (product costs) of the organization or to "support" activities (period costs) of the organization. For a manufacturing firm period costs are all costs which have no direct relationship to the manufacturing process.
Period costs are always expenses during the accounting period while product costs are inventoriable because they can be assigned to the products being produced.