Bisimulations, behavioral equivalence and logical equivalence are investigated for stochastic T-coalgebras that interpret coalgebraic logic which is defined in terms of predicate liftings. It is investigated under which conditions for the functor these notions of equivalence are related by discussing congruences for the underlying stochastic relation. It is demonstrated that logics so diverse as continuous time stochastic logic and general modal logics can be usefully approached through coalgebraic methods.