I would discourage against the use of feature layer as a generic term for file-based data sets. For most of Esri's documentation, "feature layer" has a specific meaning in the Web GIS realm, so calling a feature class a feature layer has a high likelihood of being confusing. Also, layers and data sources or datasets are very different types of objects. I think calling a shape file a feature class is less confusing than calling it a feature layer.
The larger challenge when working with Esri software is that Esri itself is not consistent in its use of terminology, and Esri even changes definitions between products some times. For example in ArcGIS Desktop/ArcMap, a table of contents was made up of layers and table views while in ArcGIS Pro you have layers and tables. Now with ArcGIS Pro, the Make Table View geoprocessing tool doesn't return a table view but a table.
Seeing that Esri can't sort out its own definitions, I think it is understandable that casual GIS users can't either.