Absorption and emission line shapes of vibrational and electronic transitions in liquids are broadened by interactions with the "bath" (in this case, the rotational and translational degrees of freedom of all the molecules in the liquid). If these degrees of freedom are treated classically, the broadening process is often known as dephasing. If; on the other hand, the bath degrees of freedom are instead treated quantum mechanically, there is additional broadening due to what is known in the chemical-physics literature as decoherence. The question addressed in this paper is the relative importance of decoherence (bath quantum effects) and dephasing. We present general developments of this subject for absorption and emission line shapes, discover several new relationships connecting classical and quantum treatments of the bath, and also consider the Stokes shift (difference in peak frequencies in absorption and emission). We next draw some general conclusions by considering a model system whose transition-frequency time-correlation function has only one bath time scale. We then consider a realistic system of the vibrational OH stretch transition of dilute HOD in liquid D2O at room temperature. For this system, we conclude that bath quantum effects are not very important, except for the Stokes shift. More generally, we argue that this is the case for many vibrational and most electronic transitions in room-temperature liquids.