This is now becoming more complicated, the urge seems to be that we eventually include all information.. I don't want to describe POW or POS, but I do need to explain the mechanism of consensus (it's the main element of trust - not the algos, those provide a mechanism that can be trusted, the consensus establishes the real world trust) without really getting technical... ie:
Computers do stuff, they then agree that the stuff was done properly. Anybody who doesn't agree, ie fails validity in the face of consensus, is considered 'bad'.
If one group of nodes disagrees with another group of nodes about the validity of a block, then there is a fork, and each node must decide for itself. Nodes that agree with you are "good" and nodes that disagree with you are "bad". That is not a consensus.
Consensus is not the main element of trust, PoW is. It is PoW that prevents a node from changing the information in the block chain. It is PoW (along with the network effect) that prevents a node from accepting an invalid block.