SAP Fiori can mean different things within a variety of contexts. Fiori can mean a series of specific design guidelines, and it can mean a collection of substantive apps. The most critical point is that SAP Fiori is driving the evolution of user interface, and it is now the forward face of SAP S/4 applications.
SAPUI5
OpenUI5 is an open source JavaScript UI library that you can use to build responsive web applications. SAP maintains the OpenUI5 code bank and makes it available to any user under the Apache 2.0 license. SAPUI5 is the proprietary sibling of OpenUI5 that SAP includes in packages like SAP HANA and SAP Cloud Platform.