I am recently working on some datasets related to traffic count stations. There were two shapefiles, one is the locations we will be working on in the fall and the other one is all the station records in the database. Both were in WGS_1984 GCS but were not projected in a projected coordinate system (PCS). So I projected them into NAD_1983_StatePlane_OHIO_South. However, after projection, the points from the two layers were not at the same location (only slight difference, but since they have the same latitude and longitude, this should not happen). So I re-ran the project tools and found that one of them used WGS_1984_(ITRF00)_To_NAD_1983 transformation and the other one used NAD_1983_To_WGS_1984_1 transformation, by default. The one with WGS_1984_(ITRF00)_To_NAD_1983 transformation did not change the locations of the points. But the other transformation, NAD_1983_To_WGS_1984_1, would move the points slightly. And I also found there are also some other transformations, like NAD_1983_To_WGS_1984_5, NAD_1983_To_WGS_1984_4. I am just curious what are the differences among these transformations? And why the project tool selected WGS_1984_(ITRF00)_To_NAD_1983 for one but used another one for the other shapefile. I checked the spatial references of the two shapefiles and believed they are identical.
The drop-down under Geographic Transformation methods shows all the relevant transformations based on the two datums. Based on the extent of the dataset, a default transformation may be selected (but it may not be the most appropriate).
Also I would prefer NAD_1983_To_WGS_1984_5 (More accurate as per EPSG) over NAD_1983_To_WGS_1984_1.
Check Choosing an appropriate transformation for more information.