Souvlaki – Wikipedia lists the variation of Souvlaki within Greece and Cyprus. Gyro (food) – Wikipedia speaks to gyros, which is the Greek evolution of the Doner kebab – Wikipedia.
In Greece, Souvlaki properly is a skewer of meat, typically pork, and often served in pita. Gyros, which involves shaved rotisserie meat (again, typically pork) is distinct from souvlaki. Either are served in small pita bread wraps, with mustard, salad, and fries.
The Cypriot version involves a pita pocket two or three times the size, tomatoes, cucumbers and cabbage, and often parsley and onion.
The Australian version diverged early, and it’s a gyros, not a skewer: you will see gyros (or yeeros) as a name as well, but souvlaki is the usual name here. (Often enough pronounced souvalaki, and more recently, as would happen with any Australian slang word, souva). Now that there is a new wave of migration of Greeks to Australia, Greek-style souvlakis are popping up as a contrast to Greek-Australian Souvlakis.
The gyros is traditionally lamb, and pork is unheard of. Chicken is the alternative meat in both Greece and Australia. The pita is twice the size. Tzatziki instead of mustard, salad, and no fries.