notes about datum conversions
1. Conversions between NAD27 and NAD83-- This converts between NAD27 and NAD83(1986) using the NADCON transformation. Newer realizations of NAD83, such as NAD83(CORS96) and NAD83(2011) can differ from NAD83(1986) by a meter or so. This conversion uses the Esri transformation NAD_1927_To_NAD_1983_NADCON.
2. Conversions between NAD27 and WGS84-- Basically this just applies the NADCON transformation from NAD27 to NAD83(1986). NAD83(1986) is the original realization of NAD83, which is practically identical to the original WGS84. The difference between the current realization of WGS84 used by GPS and the original realization of WGS84 typically is on the order of 1 meter. This conversion uses the Esri transformation NAD_1927_To_WGS_1984_79_CONUS.
3. Conversions between NAD83 and WGS84-- This converts between NAD83(2011) and WGS84(G1674), which is equivalent to ITRF08. This conversion uses the Esri transformation WGS_1984_(ITRF08)_To_NAD_1983_2011.
4. Conversions that use the same datum-- These conversions only perform coordinate system transformations; no datum transformation is defined. Therefore the datum of the output coordinates will be the same as the input coordinates.
None of the conversions involve epoch calculations to account for movement over time. If you require this level of accuracy, tools available from the National Geodetic Survey can perform these transformations.