On the surface, not much! Syrah and Shiraz refer to the exact same grape. Generally, they’re just referred to differently on either side of the Equator with Syrah north of the Equator and Shiraz south of equator, more specifically in Australia and South Africa.
Look deeper and you can see that it’s not just a difference in name, there’s a difference in style and character between the two. While both wines are assertive, the Syrah tends to be more elegant and complex but Shiraz on the other hand is more powerful and fruity, while being less layered. All this comes from the same grape which illustrates how a grape’s environment can influence the outcome and produce a totally different tasting wine.
A fun little experiment is to go to your local shop and from the shelf pick Syrah/Shiraz with the same price points but from different parts of the world. Compare them and taste what the different climate does to the wine.