Please correct me if I am wrong or misunderstanding something.
Afaik, a family parameter is never a built-in parameter.
A family parameter has been defined by the family definition in an RFA file.
Unfortunately, it can only be identified by the user display name.
A built-in parameter can always be identified by the built-in parameter enum.
Here is what I learn by browsing the Revit API help file RevitAPI.chm:
Both have a parameter definition; the Definition object is a base object for all type of parameter definitions within the Autodesk Revit API.
The definition is either an ExternalDefinition or an InternalDefinition.
Try casting to those to find out.
The InternalDefinition has a BuiltInParameter property.
The ExternalDefinition object adds properties specific to Autodesk Revit shared parameter definitions.
I hope this helps.
Cheers,
Jeremy