Yes it is true - Syrah and Shiraz are the same grape. There are many other examples of the same grape having another name in different locations (Durif and Petite Sirah, Malbec and Auxerrois, Nebbiolo and Chiavennasca), but no two names have achieved recognition world over like Syrah and Shiraz.
Syrah/Shiraz is a very versatile varietal and can produce wines of different styles. Shiraz has come to be associated with the sofy, jammy, spicy wines of Australia. Consumers expect Shiraz to have chocolate and dried fruit flavors in a medium-highly tannic and full bodied wine. Syrah, on the other hand, is expected to show more restrained black fruit components and have pepper, spice, and brambly flavors on the palate. In this case, the name on the label will give you an indication as to whether this Syrah/Shiraz was produced in a New World or Old World style.