In this talk we are going to compare two approaches (quenched and annealed) for obtaining invariant measures in open random dynamical systems. The quenched approach employs thermodynamic formalism techniques applied to a weighted transfer operator, constructing conditionally invariant measures for each fiber of the system and deriving a corresponding fiberwise limit invariant measure. On the other hand, the annealed approach relies on spectral analysis of the stochastic Koopman operator to derive a state-space invariant measure for the open system. We focus on establishing a correspondence theorem linking the results of both methods and introducing an annealed framework for a weighted transfer operator on the state space through which one can obtain an invariant measure that is absolutely continuous with respect to the conformal measure of the open system. We lastly discuss large deviation principles for the empirical measures of the killed process under both the annealed Koopman and weighted transfer operators, highlighting the role of spectral gaps in determining fluctuation behavior.