Starting in France and making its way to Australia, Syrah and Shiraz are the same thing.
When the French dark grape varietal Syrah arrived in Australia from France, the local Australians began to change its name through their accent calling it “Shi – RAZ” and eventually through actually spelling it Shiraz. Syrah and Shiraz are the same grape. Today which name a winemaker uses is based on where in the world they are making their wine.
As for the legendary Persian wine producing region of Shiraz, the Syrah/Shiraz grape seems to have no relation and the name similarities seem to be a coincidence.