Permanent Victorian Artillery Corps:
As you can see, both buttons are marked ‘BOWLEY & CO MELBOURNE’, although one is brass coloured, much polished and with a loose shank whilst the other is copper coloured and with a fixed shank. Alfred Bowley & Co were military and naval outfitters in Flinders Lane, Melbourne from c.1885 until at least 1956.
Royal Artillary uniform buttons have a crown depicted over the cannon and ramrod; this style without the crown was used for the pre-federation Permanent Artillery Artillery Corps which was created in 1870 after the use of British Corps was ceased, and lasted until 1901. (It was also used later from 1924 for Artillery Association Uniformed Staff in the United Kingdom.)
The other button of this design in my collection is by Stokes and Martin, dating it from 1870-1883.