Blockchains can be divided into different types based on their accessibility. Public blockchains are open public networks that allow anyone to download the blockchain software and become a node if they satisfy the computing requirement.
There is a restriction on who can become a node in the consortium blockchains. So, permission is required for anyone desirous of becoming a node. Consortium networks are also called shared permission. This is restricted to a few and the transactions are not open to the public, but it can allow competing authorities to participate. Therefore, in this type of network, the degree of trust is low.
Private blockchains are more like a centralized system with a higher degree of trust. Transactions are highly auditable and those with access can view them. The transactions are so auditable that they can be traced to those engaged in the transaction. These are like traditional databases to some extent but with added security features of cryptography. These are also called permission blockchains.
