The atomic spectrum is more like the transitions of electrons among electronic energy levels in an isolated atom. Atomic spectrum is mainly affected by interaction of the transitioning electrons between the nuclei spins and between the other electrons in the same atom.
However, molecular spectrum involve transition of electrons in molecules with two and more atoms(it can be in the same or different). Also, the valence electrons are now in different orbitals than that of the atomic orbitals and the orbital structure has changed the electronic transitions are different
