Analytics Platform System (APS) is simply a renaming of the Parallel Data Warehouse (PDW). It is not really a new product, but rather a name change due to a new feature in Appliance Update 1 (AU1) of PDW. That new feature is the ability to have a HDInsight region (a Hadoop cluster) inside the appliance.
So APS combines SQL Server and Hadoop into a single offering that Microsoft is touting as providing
Big Data In A Box
Think of APS as the “evolution” of Microsoft’s current SQL Server Parallel Data Warehouse product. Using PolyBase, it now supports the ability to query data using SQL across the traditional data warehouse, plus data stored in a Hadoop region, whether in the appliance or a separate Hadoop Cluster.