They are the same cut.
Quoted from Meat 102: Cuts, Anatomy & Preparation (emphasis mine):
Some restaurants will call the ribeye a “tomahawk steak” if the entire rib bone is left on and french cut by the butcher, since it then looks like a small hatchet. It is common for butchers to cut the bone down a bit, however, for packaging purposes ... Sizes and portions range from anywhere between 14oz to 36oz, most often hovering around the 20oz mark in restaurants.
36 oz is about 1 kg, or half as large as the "Australian Tomahawk" -- which can be attributed to having the full rib bone, as well as probably a thicker cut (and a generous pinch of marketing-speak and publicity).
The Tomahawk is one of largest steaks in Australia, weighing in at
1.3kg – 3.6kg (1.8kg average). Each Tomahawk is a rib-eye, or scotch fillet on the bone...
(see also StockJournal article)
EDIT: It's also called a cowboy steak or cowboy chop. So, the uncut rib bone seems to be the primary difference between "Australian" and "US" tomahawk steak.