The earliest synods were not standing institutions at all but one time gatherings called to settle a specific dispute, and the dispute that produced some of the first recorded examples was the dating of Easter. Toward the end of the second century, bishops in Palestine, Pontus, Gaul and Rome each convened local meetings, reported by the historian Eusebius, to argue that the wider church should follow their own region's custom rather than the Quartodeciman practice kept in Asia Minor. The pattern generalized: a synod met because a question had arisen that a single bishop could not settle alone, and the largest synods, drawing bishops from across the whole Christian world, became the ecumenical councils, the first at Nicaea in 325. What synods since then can actually decide has never been uniform.
The Church of England's General Synod, established in 1970 to replace an earlier Church Assembly, passes measures with the force of law once Parliament approves them. Roman Catholic synods of bishops, instituted after the Second Vatican Council in the 1960s, exist to advise the pope rather than to legislate on their own authority. The same word, applied across traditions, can mean a legislature or a committee, and only the specific body's own constitution says which.