In plain and simple terms - Syrah and Shiraz are both the same grape varietal (originally), but the name gives you a clue to the 'Terroir' (location, climate, soil) that the wine has come from and the style in which it has been made.
Syrah is a red grape varietal traditionally grown in the Rhone Valley of south-eastern France. Since then it has spread to many places around the world including California, Argentina, Chile and more recently, South Africa and New Zealand.
The place that has taken the grape varietal to its heart is Australia. But in true Australian fashion due to climate, soil and culture the wines have taken on a new personality, character and even a new name.

 

The difference in Syrah & Shiraz stems from the different expression and reflection of the Terroir, vintage as well as other viticultural practices, and also winemaking techniques chosen. The Syrah/ Shiraz grape was once thought to have originated in Persia (plus many other romantic stories and journeys over the centuries), but recent research, DNA testing indicates the grape is a native of the Rhone Valley, in France. In 1999 they found Syrah to be the offspring of two obscure grapes from southeastern France, Dureza and Mondeuse Blanche. Syrah it is best known for its usage in Hermitage, in the northern Rhone.
If an Australian winemaker was to label the wine Shiraz, you can expect a full-bodied, rich, ripe, fruit driven style of wine, with high alcohol - the Australian way.
'Syrah' on the other hand tends to emphasize earth and subtle spice and slightly more delicate notes due to a cooler and longer growing season found in France and also selected regions in New Zealand.
Definitely try them both; they each have their rightful place in your cellar and on your table and both are interesting and rewarding when matched with the right cuisine and when served in the correct Riedel stemware. Both Syrah and Shiraz can age extremely well, plus if enjoyed in their youth, will appreciate as with all well made red wines - decanting for a period of time before serving.