The difference between these two lights is the intensity with which men perceive them with their natural eyes. This is the literal sense that the mind perceives it and according to Plato, knowledge can only be perceived. The light that emanates from the fire is of low intensity since it is only perceived through our senses which we can only imagine in our constrained state. The fire is so limited that not much can be learned from it since the men in the cave are accustomed to it. Consequently, any knowledge emanating from the fire is limited because it is simply there and one does not need to do anything to acquire it. The light is a representation of learning through mind perception which in itself is not enlightening and cannot add new knowledge to man.
The light of the sun on the other hand is quite intense and when let out on a person that has been living in darkness can cause partial blindness. In other words, Plato uses this light to show the difference between low learning through mind and higher learning through the soul. Learning through the soul is the ultimate learning which is only possible by making the efforts and aspiring to learn. Due to its limitations, it requires the learner to rid himself of the various constraints that limit learning to the realms of perception of the mind in the physical state. This learning is more revealing and enlightening which overrides other knowledge which is acquired through our feeble minds. Unlike knowledge that is gained through habits and patterns like in the case of the light of the fire, knowledge from the light of the sun has no shadows but lays bare all the fundamental truths about different concepts of nature.