I have two shapefiles with different projections. When I load both into ArcMap I get the 'Geographic Coordinate Systems Warning' when the second is loaded into table of contents but they both align properly with one another. If I export the second one using 'export data' than choose to export it using the coordinate system of the data frame, this exported feature has the same projection as the first shapefile and aligns with it properly. But if I project the second shapefile using the toolbox I have to choose a 'Geographic Transformation' and this output doesn't properly align with the first shapefile.
Can anyone explain the difference between these to methods to change the coordinate system of a shapefile?
Why would I used the projection toolbox if it has to preform a Geographic Transformation and shift it retaliative to other features as opposed to changing the data frame projection and exporting it?