Since there are so many Blockchains out there, it is important to distinguish the different kinds. In the following articles, the terms public, private and consortium are defined, clarifying some of the common misunderstanding that exists around Blockchains today.
The below articles make some key distinctions about the nature of different Blockchains. At FXCH we are using a consortium-style Blockchain which is especially useful for permissions.
Vitalik Buterin on Misconceptions in the Private vs Public Blockchain Debate