True Cross said to be the same as instrument of Jesus' crucifixion
The True Cross is said to be the real cross that Jesus of Nazareth was crucified on, according to Christian tradition. 
It is related by numerous historical accounts and legends, that Helena, the mother of Roman Emperor Constantine the Great, recovered the True Cross at the Holy Sepulchre in Jerusalem, when she travelled to the Holy Land in the years 326–328. The late 4th-century historians Gelasius of Caesarea and Tyrannius Rufinus wrote that while she was there, she discovered the hiding place of three crosses that were believed to have been used at the crucifixion of Jesus and the two thieves, Dismas and Gestas, who were executed with him. To one cross was affixed the titulus bearing Jesus' name, but according to Rufinus, Helena was unsure of its legitimacy until a miracle revealed that this was the True Cross. This event is celebrated on the liturgical calendar as the Feast of the Exaltation of the Cross.
The Catholic Church, Eastern Orthodox Church, Oriental Orthodox Church, and the Church of the East all claim to possess relics of the True Cross as objects of veneration; while Protestant and other Christian churches generally dispute the authenticity of the relics, and do not hold them in high regard.Socrates Scholasticus
In his Ecclesiastical History, Socrates Scholasticus (born c. 380) gives a full description of the discovery later repeated by Sozomen and Theodoret. In it he describes how Helena Augusta, Constantine's aged mother, had the pagan temple destroyed and the Sepulchre uncovered, whereupon three crosses, the titulus, and the nails from Jesus's crucifixion were uncovered as well. In Socrates's version of the story, Macarius had the three crosses placed in turn on a deathly ill woman. This woman recovered at the touch of the third cross, which was taken as a sign that this was the cross of Christ, the new Christian symbol. Socrates also reports that, having also found the cross's nails, Helena sent these to Constantinople, where they were incorporated into the emperor's helmet and the bridle of his horse.