One reason buying a mobile phone plan is so complicated is that there can be several different companies involved (often referred to as ‘providers’) or the same one could provide the network, service and billing.
Optus, Telstra, 3 and Vodafone are called carriers: they own, operate and install network infrastructures for mobile phone services.
These companies supplement and compete with the carriers by buying services from them and repackaging them for sale to you. They may provide customised billing, and generally have more personalised service and a greater range of plans.
In a mobile phone shop you can generally buy a range of phones and plans. However, the contract is with the service provider or the carrier, not the retailer.
The call plan
This is how you connect to the network, and it may be with a carrier or via a service provider.