Indeterminate hires are permanent hires. So it's a permanent position in the public service.
A term hire is an engagement, a hiring in the public service for a specified period of time.
A casual hire is a hire that is for 90 days only. An individual can only be working in a department for 90 days per year. There is no merit test for casual hires. So casual hires can be done in a very casual way, if you like. There is no process required around casual hires.