No. Generally, theoretical moments are the one computed based on the state space representation of the solved model. See e.g. Hamilton (1994): Time Series Econometrics. These moments are computed at the parameter vector given, i.e. either the calibrated ones when running stoch_simul directly or the one from estimation if running stoch_simul after estimation.
Simulated moments are based on simulation from the model solution for a specified period of time. If you run sufficiently many periods, the simulated moments will converge to the theoretical moments (asymptotically).
There is no general rule what is better to compare. Several short simulations of the same length as your actual data or the theoretical moments. I would personally go for the latter.