Blockchain can be divided into several types based on different criteria.
Based on ownership : Public, Private and Consortium.
Based on permissions: Permissioned and Permissionless.
Based on support for programming: Turing incomplete and Turing Complete.
These type of blockchains are not owned by any single person or organizations.
They are public and anyone running the blockchain can become a node of the blockchain network.
All nodes have a copy of blockchain and can participate in mining and auditing process.
in these type of blockchains the transactions are verified and added to blockchain using decentralized consensus mechanisms.
Examples of public blockchain are Bitcoin and Ethereum
These blockchains are owned and controlled by a particular individual or organization.
That is, they are open only to a consortium or group of individuals or organizations who have decided to share the ledger among themselves.
There are various blockchains now available in this category, such as HydraChain and Quorum.
Optionally, both of these blockchains can also run in public mode if required, but their primary purpose is to provide a private blockchain.
These type of blockchains are not governed by a single person or organization.
They are controlled by a group of Organizations.
All the transactions are verified by all or some of the particapating memebers of the different organizations.
Examples of these type of Blockchains are r3 and EWF