1
"Distributed" means operating on more than one devices which dont share physical memory and perform their task (which might be storage or computation) to perform one single task (which in our case might be to have same copy of ledger)
"Consensus" means when everyone is on the same page.
So,"Distributed Consensus" means we want all the different devices on the network which dont have a shared memory and communicate by message passing mechanism to have same copy of ledger. Is that correct ?
2
Yes, you are correct. In addition, we assume that there are adversaries which can operate arbitrarily and replace some honest-looking devices on the network and make them behave like a "malicious intelligence". They send data adversarially designed to disrupt your protocol.
You want your "distributed consensus" to be able to work under these conditions.
Furthermore, if an arbitrary number of such malicious devices can be injected and you cannot tell devices apart, we call it "anonymous distributed consensus", the problem that bitcoin is solving.
