Datums - History
In 1966 the Australian Geodetic Datum was derived and this is specified by a radius and flattening for the earth.
The AGD coordinates are in terms of Latitude and Longitude.
The Datum was known as AGD66 meaning that it was the 1966 adjustment of the primary geodetic network.
The Universal Transverse Mercator projection was then used to derive X-Y coordinates and these coordinates are
known as The Australian Map Grid (AMG).
In later years the primary network was readjusted and hence you have AGD84 etc., so the first three characters
define the grid(or datum) and the rest is the date of the adjustment of the primary data for the area.
In 2000 Australia adopted a new geodetic datum to fit with a world based datum (WGS84) which had a different
radius and flattening.
This datum was called "the Geodetic Datum of Australia" (GDA) and the UTM projection based on this was called
the Map Grid of Australia (MGA)
So technically, if we are stating Transverse Mercator coordinates we should refer to AMG or MGA
If we are stating Latitude/longitude we should use AGD or GDA.
If you are in any doubt, you can look at what is written in the projections files.
For AGD the radius is 6378160 and the reciprocal of the flattening is 298.25
For GDA the radius is 6378137 and the reciprocal of the flattening is 298.257222101,