What is the difference between SAP HANA and SAP S/4HANA?

SAP HANA refers to SAP's newest database - HANA = High-Performance Analytical Appliance. HANA is an in-memory database (meaning the data resides in the server's memory as opposed to the server's hard drives). It allows the real-time processing of very large amounts of data in a very short amount of time. 

SAP S/4HANA, on the other hand, refers to SAP's newest release of its ERP system (Enterprise Resource Planning). The S/4 system only runs on the HANA database, as opposed to previous SAP releases that also ran on different databases (such as Oracle, IBM, or Microsoft databases).