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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,

GDA2020 Datum
The difference between GDA94 and GDA2020 coordinates is mainly due to plate tectonic motion and it also has a smaller distortion component.
The distortion component is attributable to several second-order effects, such as an improved realisation of the global reference frame over time; irregular ground movement since GDA94 was established; and improvements in computation methods since GDA94.
These effects vary in magnitude and direction around the country and can be as large as ~0.5 m.

The transformation can be carried out using a formula (a 7 parameter similarity (Helmert) transformation).
This models the plate tectonic movement which is approximately 1.7m NNE over 26 years.

Alternatively it can be done using one of the two 2D national transformation grids:
Conformal: This is a grid version of the formula
Conformal + Distortion: incorporates the formula plus localised and regional distortion.

These grids are downloadable from the ICSM GitHub transformation grid repository.
Advice on choosing which grid to use is included in Table 3.4 in in the GDA2020 Technical Manual available at GDA2020 Technical Manual