I'm trying to figure out what you mean by 'WGS 1984 Geographic Coordinate System, Version 2'. There's no such coordinate reference system (CRS) by that name in Esri software.
Meanwhile, a long time ago in a software not so far away, we added ESRI::102113, "WGS 1984 Web Mercator." The name is unfortunate, because the geographic CRS used was actually a variant of WGS 1984 (EPSG::4326) in that it used a sphere with radius = 6378137.0 m. Its name is "WGS 1983 Major Auxiliary Sphere." This was prior to version 9.3.
People didn't like it because the geographic CRS wasn't the standard WGS84 so there were issues with having to transform from a local GeoCRS to WGS84 and then to the sphere-based WGS84. One nice thing about this definition is that it used the standard Mercator algorithm, with the sphere equations triggered by the GeoCRS.
About the same time, EPSG added a similarly designed projected CRS, EPSG::3785 (sphere-based GeoCRS).
Esri then added a new Mercator algorithm, Mercator (auxiliary sphere), which defaults to using a major aux sphere (radius = semimajor axis) and supports a few other spheres. That enabled Esri to add 102100, which uses the standard WGS84 definition, but a new Mercator algorithm.
Again, about the same time, EPSG deprecated (made obsolete) 3785 in favor of 3857, which again similarly to ESRI::102100, uses the standard WGS84, and a new Mercator algorithm.
Esri then "code-changed" 102100 to 3857 to keep up with the EPSG registry/dataset. Because older servers wouldn't understand 3857, we still often publish services with the older number, 102100.
So, all 4 of these well-known IDs: 3785, 3857, 102113, 102100 will give exactly the same results. If you unproject values from any of them, the results are EPSG::4326.
Note: EPSG randomly assigned WKIDs. They did not try to confuse people by using 3857 as a replacement for 3785. It was just weirdly random.
Disclaimer: I'm an Esri employee and am on the geodesy subcommittee that maintains the EPSG registry, although I was not a member of the subcommittee until after they added 3857.