Hi @dypisgood In my humble opinion, no.
Deterministic Steady State: when we want to compute the conditional welfare, usually we start/perturb the economy from this type of steady state. At the steady state, there are no shocks.
Risky Steady State: despite no shocks, the agent observes the distribution of the shocks that may hit the economy in future, e.g. standard deviation \sigma. In this context, we simulate long sequences of endogenous variables at a higher order to see they will converge to the risky steady state or the stochastic steady state.
Ergodic/unconditional mean: We get this value by simulating the economy with shocks after a long-run period to compute the unconditional welfare.