WGS 84 - NAD 83 with a twist

I have a dataset of GPS field point collected received in WGS 84 but displayed in NAD 83 UTM. I used a field point to inform a total station for a reference starting point, so all my total station data is also displayed in NAD 83 UTM (though based on data collected in WGS 84 and displayed in NAD 83).

I then went through a process of differential corrections for the field points, and the data is displayed in WGS 84 alt/longs. I now need to "correct" my total station data based on the new points, but my corrected points are in WGS 84 lat long and my total station data is in NAD 83 UTM. Would it be best to project the corrected points into NAD 83 UTM, or to project the total station NAD 83 UTM displayed data as WGS 84? Could someone help walk me through the process?