Digital Publishing Solution, also known as DPS2015, is a content-focused publishing mechanism. You can create content a number of different ways, but there's kind of a focus on templates and having content automatically feed in from a CMS.
Digital Publishing System, also known as DPS Classic, is a design focused publishing mechanism. You use InDesign to create pixel-perfect layouts that then get published into apps.
It's kind of an oversimplification, but DPS Classic is kind of like "print replica" and DPS 2015 is flowing content that can be automatically updated without human intervention.
I sincerely doubt this will be on your exam, but good luck