The Bernini Fountain: This fountain was created by Gian Lorenzo Bernini between the years 1667 to 1677. The fountain was commissioned by Pope Clement X. The construction of the fountain took Bernini ten years and no detail was forgotten. Bernini's design was influenced by his earlier designs.
The fountain is located on the south side of St. Peter's Square.
Maderno Fountain: The fountain on the left, when facing St. Peter's Basilica, was designed by Carlo Moderno. In 1612 Pope Paul the V rebuilt the ancient Roman aqueduct and it was renamed the Acqua Paola. The newer aqueduct provided the fountain with a larger source of water.
this fountain was redesigned by architect Carlo Maderno after being commissioned by Pope Paul V.The architect Carlo Maderno was the nephew of the architect Domenico Fontana. He built a base for the fountain on top of which a large basin was placed. The basin is decorated with steps and small columns. Maderno left the large lower stone vasque of the old fountain. He then decorated the pedestal on top of it with four scrolls of stone. The new design has a large lower stone vasque, which the old fountain also had. He removed the small upper vasque, and replaced it with a mushroom like cap with stone scales. When the water flows from the top it pours down over the upper vasque and the light shines through it.
The source of water for the fountain was on a hill. This caused the water to shoot upwards by the power of gravity. In 1641, this fountain was said to be the most beautiful fountain in the whole of Europe.
from http://vatican.com/photos/gallery/st_peters_square_fountains-p40