This is primarily a question about something I heard Vitalik Buterin say in an interview the other day. (Unchained podcast's January 9, 2018 episode, at 34 minutes, 15 seconds) I quote:
As far as the cons [of proof-of-stake], I would say the main one is that it is a different security model. It’s a different security model that basically says that, in order to securely authenticate the blockchain, you have to log on to the internet at least once every few months. And if you don’t do that, then in order to bootstrap yourself to the chain again you basically have to trust some group of people who have. And I think that in reality this is a totally fine security model because people basically already trust this security model for software updates.
I don't understand this quote. The way I understand it is that, regardless of proof-of-work (PoW) or proof-of-stake (PoS), a person has two choices: Run a full node, or run a "lite" node where you trust a third party node.
If you run a full node, you have to download all of the chain before you can create new transactions. If you run a lite node then your balance and transactions are dependent on the third party, but you don't have to wait to download the chain. It seems to be that way both for clients of both PoW and PoS blockchains. So I don't see how the consensus algorithm is relevant. The only explanation is that I'm completely misunderstanding the quote, so I'm hoping that someone can shed some light on my misunderstanding.
Note: This question is not asking if PoW is better or worse than PoS. I just want to understand the quote. Thank you.