deterministic vs stochastic?

[Peterpierre]

what is the difference between solving with Dynare:

1. a stochastic model linearized to the first order (ie, certainty equivalence so the expectation of the shocks is zero and their variance is irrelevant to compute the policy functions) then simulating the impulse response (ie, the reaction to a one time shock)

2. solving a deterministic model that starts in the steady state of the previous model and has a transitory shock lasting only the first period (ie, the model converges to the same Steady state)

why the two methods should not give the same Impulse Response?

Thanks a lot