the crystal field of materials can lead to the splittting of the ground and excited state energy level into a lot of Stark levels. under lower tmperature, the absorption comes from the lowest Stark energy level of the ground state to all Stark energy level of excited state. the emission comes from the lowest Stark energy level of the excited state to all the Stark energy levels of the ground state. so, the strucure of a materials can change the absorption and emssion spectra.
After absorption prior to emission happen relaxation. As the gentleman without sense of humor noted, there are tons of material specific literature on the subject.