Technically, NAD 1983 aka North American 1983 should be used for data that's on the original NAD 1983. NAD 1983 was released in 1986 and is valid up at least until a state did a HARN re-adjustment. Illinois' was around 1997 (from the GEOCON operator's guide, page 13).
The continuously operating reference station (CORS) started around then, thus CORS96.
If you took the data that is labeled with the standard NAD83 and then start applying geographic transformations to it, the data will be offset at the centimeter/decimeter level because the transformation doesn't need to be applied. It will also affect which existing transformations are available for us.
I believe distance and area calculations will effectively be the same. Generally between the two systems, all points will be offset about the same.
Extra note for others: 1201 is a zone number in the US State Plane grid system and represents a transverse Mercator-based projected coordinate reference system that is based on one of several different geographic coordinate reference systems.
Note: I work for Esri.