So from what I understand, Bitcoin's PoW is prone to 51% attack, but as a distributed system it is also prone to BFT's 1/3 attack right? I think it's mathematically proven that in a distributed system, if you have more than 1/3 bad nodes collaborate together, then you cannot safely reach a correct consensus no matter what?
So for Bitcoin, there are two types of possible attack scenarios, one is if a miner node consistently has more than 51% computing power of the whole network then it can double-spend indefinitely and basically has unlimited cash to spend.
The other is if more than 1/3 of the nodes in the whole network are bad guys working together with modified malicious node code then they can potentially stop the correct block being accepted and make it impossible for others to know which is the correct longest chain, thus prevent valid transactions being processed and recorded.
So are my understandings correct?