DPS Classic publishes folios (ie: an 'issue') into a classic app. This app is fixed layout - ie: has a generic look like all other Adobe DPS Classic apps. You can also add an html kiosk storefront to the binary app, to enhance the main home screen, however this can be time-consuming and costly. You can use Indesign CC to create your layouts, or HTML, or PDF. And you still have to use the Folio Builder to create your issues. And then publish via the Folio Producer. A good example is the current UK Wired magazine, or GQ UK, and BBC Top Gear. Once you submit your app to Apple or Google etc, that's the app locked down until you next submit. Adobe will continue to support this system for the time being as far as I understand it - but I would advise moving up to the new 'Solution', as its totally brilliant, and that's where their focus will be from now on, I am sure.
DPS 2015 (Adobe's new Digital Publishing Solution) is a new way to publish digital content - you can publish single articles, collections (groups of articles). You can also feature banners, and the app main browse paage can be changed as many times as you like. For example one can update on an minute-by-minute basis - ie: create a news feed, and also change your browsing pages as you see fit. Its highly flexible and offers much more compared to Classic. You can use HTML via a variety of solutions via the DPS Content API - Wordpress, Woodwing Inception, Drupal, and loads more CMS solutions, giving you more flexibility in the tool that you use in your organisation. You can also use Indesign of course, and also PDFs. Great examples of the new DPS 2015: Qantas, Swiss Air, The Times, Shell. The browse pages are designed using the innovative Layouts and Cards feature - and its all 'live' - meaning the customer sees a more enhanced, freshly updated experience. You can also choose to publish to phone, tablet or both. Its flexible dependant on your needs...
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