Child Theme: Simply a duplicate of your blank website which you create before you begin your web design project. Creating one will save you from recreating site customizations to your header, footer and CSS if you update the theme.
Premium Child Theme: A Child Theme that you pay for, which comes with fully designed pages, posts, and design customizations that simply needs your images and copy and other minor tweaks. Often a Premium Child Theme will have customization elements that would be difficult for you to replicate on your own, thus you pay for these customization elements. There are a variety of premium themes found in the Elegant Marketplace Shop, each which have elements suited towards specific businesses or design needs.