You're correct that the original NAD83 and WGS84 were considered coincident, but that was 30 years ago and both have moved on. Pun, probably intended.
WGS84 has had several re-adjustments/realizations to keep it in line with the International Terrestrial Reference Frame (ITRF) until the current version is probably within a cm or so. The realizations are identified by the GPS week that they were defined in: G730, G873, G1150, G1674, G1762.
Meanwhile, NAD83 is tied to the North American plate, so it's been drifting farther from WGS84 and ITRF over time.The National Geodetic Survey has also done several re-adjustments/realizations: HARN, CORS96, NSRS2007, 2011.
Esri added the WGS84 realizations only recently for ArcGIS Desktop 10.5.1, so every transformation has been to a "generic" WGS84 version. To compound issues, unless you're US military or contractor or ally, you don't get accurate WGS84 coordinates. You either have general coordinates, or if the data went through any RTK or post-processing, it was aligned with the control points that were used--usually either an ITRF system or some realization of NAD83. At that point, the data is in the same coordinate system as the control point network, but software sometimes doesn't say that.
Melita