What is the difference between limbo and purgatory?

Purgatory is believed by Catholics to be an intermediate place for souls that have died in God's grace but who yet have a debt of temporal punishment due to sins that they must make satisfaction for in justice before they can become fully purified and thus enter Heaven. Purgatory will end with the passing of this world. This is a doctrine of the Catholic Church.

Limbo is traditionally believed by Catholics to be a place for souls who never attained the use of reason before death and who have not been baptized and so are bereft of the saving mark of grace upon their souls that is conferred at baptism and which allows them to enter heaven. These souls could not enter heaven since they are still stained with Original Sin. However, because they have committed no personal fault of their own, they are certainly not condemned to hell. As a result, these souls are placed in Limbo, a place of natural happiness, much like the well-being felt when things are going well for someone on earth. Limbo is thought to be perpetual, and will remain after the end of the world. The teaching on Limbo is a theological opinion, which means the exact nature of Limbo or unbaptized infants is not conclusively known. Recently, the Vatican approved a document called "The Hope of Salvation for Infants Who Die Without Being Baptized" which seeks clarification on the theological opinion concerning Limbo with some concerns ranging into whether it even exists. The impetus of this inquiry is that many find it difficult to believe, especially with abortion so prevalent, that unbaptized infants are barred from heaven from no fault of their own. Future statements can probably be expected on Limbo and its status and the pope may even make an authoritative declaration on how this topic is to be viewed by the theological community of the Church as well as taught in catechism.