The differences between public non-permissioned blockchain networks and private permissioned blockchain networks have been well chronicled. In brief, a public permissionless blockchain has no access restrictions to view its data or participate. Usually, such networks offer economic incentives for those who secure them and utilise some type of lottery-based consensus algorithm. Some of the largest, most known public blockchains are Bitcoin and Ethereum.
A private permissioned blockchain network requires permission to read the information on the blockchain and limits the parties who can transact or participate. Some examples include R3’s Corda, as well as various Hyperledger frameworks, including Hyperledger Fabric and Hyperledger Sawtooth among others. There are few cases, if any, where a private permissionless network would make sense, but there are some examples of public permissioned networks appearing to facilitate better scaling of public networks.