For the sake of completeness, one might add that instead of logging inputs or states, you could also store outputs. Given a deterministic statemachine will allow you to derive the list of consecutive states and thus inputs from that.
Of course, storing outputs is not what you want :)
Yes, there are lots of subtle variations. In practical implementations, we'd tend to store all three: inputs, state, outputs. But we'd be recovering only from one of them. The others would be debugging logs.
EOS at least will store the incoming messages and the outcoming messages. And if the outputs become inputs into a later contract, they are referenced again.