These terms, pronounced (rare-a-dos & ret-a-bull) are often interchangeable and refer to any screen or other structure immediately behind the altar and usually attached to the altar wall.
These edifices, first introduced in the twelfth century, were originally decorative in nature, depicting scenes from the Gospel or the lives of the saints.
As they became more embellished and ornate, the simple screen gave way to more sturdy and lofty structure, often reaching to the height of the sanctuary ceiling and appointed with reliquaries (places where you might find the mummified finger of St. Swithin, or the sacred toenail of St. Brigid) and sometimes life size statues of Christ or the Virgin Mary.
After the reformation in the sixteenth century, when reliquaries and representation of Jesus and the saints fell out of fashion, the reredos/retable was restored to its original simplicity.
Nowadays, the reredos refers to any structure that is attached, or rests close to, the altar wall, and is either decorated-as described above- or serves the practical function of providing a home for the altar cross or other liturgical ornaments.
The informal, modern distinction between a reredos and a retable is the place where the altar cross resides and is also home to the aumbry (the place where the reserved sacrament is kept.)
This change in function reflects change in our understanding of what is to be revered and how that reverence finds its expression in our architecture.
For, whereas, before the reformation, a reredos might be home to the dead remains of some long forgotten saint, in our reredos it is only the living body and blood of Christ, which holds that place of honour.