Worthington Proper means the City of Worthington... I think. I know I noticed hearing and seeing "Worthington Proper" when I moved to Central Ohio in 1990. You don't hear people talking Dublin Proper or Westerville Proper yet much of their school districts are outside of the Dublin and Westerville Corporation Limits. Or maybe you do... I don't.
I believe Worthington Proper means within the corporation limits of the City of Columbus. Because there is a vast expanse of Columbus in the Worthington schools as well as homes in unincorporated areas including the Village of Riverlea there are many Worthington area homes which are not in Worthington Proper...
I heard someone use "Worthington Proper" recently.
Worthington Proper = Corporation Limits, the City of Worthington
Old Worthington = a neighborhood that was the original Village of Worthington
City of Worthington neighborhoods (Worthington Proper) including:
Some Worthington area neighborhoods that are Not Worthington Proper but lovely neighborhoods none the less!
Deercreek (or Deer Creek)
Especially the list of Worthington area neighborhoods is just a smattering of the Central Ohio neighborhoods in the Worthington area or Worthington schools... nothing improper about them... just not in the City of Worthington!