Hi Amara,
Fiori is the design principles, and the design style guide that underpin the new apps. You find these here:
https://experience.sap.com/fiori-design-web/
An app is said to be a Fiori app if it follows the design principles and uses elements in from the design style guide in the intended way. Official delivered Fiori apps can be found in the Fiori Apps Library Fiori Apps Library However we generally refer to customer or partner built apps as Fiori apps if they also respect the design principles and style guide.
The Fiori Apps Library explains what technology is needed for each app.
The primary technology used for Fiori is SAPUI5.
There are free openSAP courses on both Fiori and SAPUI5 where you can learn.
Developing Web Apps with SAPUI5 -
SAP Mobile Platform was an older on-premise approach that predated Fiori and SAPUI5. While still viable, there are additional server, licence and resource/skill requirements that make it a less attractive option for most customers. Some of the additional functionality that were previously only available via SMP - such as offline apps and push notifications - are now available using Fiori/SAPUI5 in conjunction with HCPms (HCP mobile services) at a subscription price.
You can also find out more about the differences on openSAP Developing Mobile Apps with SAP HANA Cloud Platform - Jeff Gebo and Dhimant Patel
Good luck!
Rgds,
Jocelyn