A permissionless blockchain is an open-source blockchain and it is decentralized as well. Anyone can join the network and participate in the consensus and validate the block. Anyone can mine, anyone can run the nodes and it does not involve a central authority. It is potentially as wide as the internet. Bitcoin is a classic example of permissionless blockchain.
A permissioned blockchain has a central authority who assigns the responsibility to the users to run the blockchain and maintain the network. Not everyone is authorized to join the network, only selected people are allowed to join the network. Further it may go for an identity check of the participants in the network. It is potentially not as wide as internet. Banking institution generally show their interest in this kind of blockchain.
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