Richard Fairhurst, I agree completely with your second paragraph, i.e., the OP is overlooking the importance of Resolution, Tolerance, and the reality of computational precision.
Regarding ArcPy, it offers very little native functionality that isn't part of the core ArcGIS product. ArcPy is a Python wrapper around all of the code that drives ArcGIS for Desktop, ArcGIS Pro, etc.... Looking through some of the files that make up the site package:
...\Desktop10.4\arcpy\arcpy\arcobjects\geometries.py
from arcpy.arcobjects.arcobjects import Geometry
...\Desktop10.4\arcpy\arcpy\arcobjects\arcobjects.py
class Geometry(mixins.GeometrySpecializationMixin,_BaseArcObject):
"""Geometry objects define a spatial location and an associated geometric
shape."""
def getArea(self, method="GEODESIC", units=None):
from ..geoprocessing._base import gp_fixargs
return convertArcObjectToPythonObject(self._arc_object.GetArea(*gp_fixargs((method, units))))
Area calculations with ArcPy Geometry come from ArcObjects and are converted back to Python. There may be more than one set of geometry calculations within ArcObjects, and if there is they may not return the exact value in all circumstances, but that would be caused by differences in ArcObjects and not a difference between doing the calculation with Geometry Calculator versus ArcPy.
