The difference between multi-sig and no private key is that the former is an implementation of the blockchain protocol (e.g. different in Stellar and Ethereum) while the latter is a generic algorithm/service. Different layer.
Yes, I just meant that in practice the risks are the same from a security perspective (and most legit blockchains support multi-sig at this point), especially for the shares so I wouldn't call it 'no private key' :D
