The difference between a Fiori and a Fiori-like app is quite simple: Trademark Issues.
Both "types" share or are limited to the same technics, libraries, mechanisms and design rules like certain UI5-libraries, OData as the main Model within the Model-View-Container (MVC) concept, responsiveness of the UI...
SAP itself never mentioned any problem with naming or categorizing your app as a Fiori App, as far as I know. But to get some distance to the original SAP Fiori Apps its some common sense within the community to call your own App, which respects the mentioned technics, libraries, mechanisms and design rules, a Fiori-like app.
Have Phun
Silvio