(b) That's correct. Historically, private ownership of land was not registered in Australia. A person's right to land could only be proved if they possessed documents showing each transfer of the land from the first (colonial) owner onwards - that is, the 'chain of title'.
From 1858 onwards, legislation was enacted throughout Australia which established a system of registering land interests. This system is known as the Torrens system, named after Sir Robert R. Torrens, who first introduced the system in South Australia. The Torrens system relies on the registration of land ownership in a central register kept in each Australian jurisdiction. The applicable rules are now found in legislation.
Most land in Australia has a record (or 'folio') in the relevant central register where ownership of that land is recorded. We call such land 'Torrens system' land. The register is publicly searchable, and from the register it is possible for the owner of a parcel of land to get a document confirming their title. This is known as the 'Certificate of Title'.
However, even today not all land in Australia is registered. Those areas of land not governed by the Torrens system are still subject to the old common law rules about land ownership. Such land is known as 'old system' or 'general law' land. But most land in Australia, especially for business purposes, is Torrens system land and, for the remainder of this module, you can assume it is Torrens land being referred to unless otherwise stated.