We address topics related to molecules coupled to quantum radiation. The formalism of light-matter interaction is different for classical and quantum fields, but some analogies remain, such as the formation of light induced crossings. We show that under particular circumstances, the molecular dynamics under quantum or classical fields produce similar results, as long as the radiation is prepared as a Fock state and far from ultra-strong coupling regimes. At this point, the choice of specific initial Fock states is irrelevant since the dynamics scales. However, in realistic multistate molecular systems, radiative scaling may fail due to the presence of simultaneous efficient non-radiative couplings in the dynamics. Polar molecules have permanent dipoles, and within the context of the full quantum Rabi model with a Pauli-Fierz Hamiltonian, they play a crucial role in the polaritonic dynamics since both permanent dipole moments and self-energy terms produce drastic changes on the undressed potential energy surfaces at high coupling strengths. We also gauge the effect of including rotational degrees of freedom in cavity molecular photodynamics. For diatomic molecules, the addition of rotation amounts to transform (both with classical or quantum fields) a light induced crossing into a light induced conical intersection. However, we show that conical intersections due to molecular rotation do not represent the standard properties of well-known efficient intrinsic conical intersections inasmuch they do not enhance the quantum transition rates.