From my understanding, both Thureophoroi and Thorakitai fulfilled similar roles as "medium" infantry in a Hellenistic army.

A proper Hellenistic army, on paper, would consist of a central Phalanx line of Phalangites, a skirmishing force of Peltasts, cavalry, and in the later eras, the medium infantry like Thureophoroi and Thorakitai.

The Phalangite Phalanx was very powerful from the front, but exceptionally long pikes coupled with their very large, dense formations meant that they tended to be somewhat unwieldy.

The Peltasts were typical light skirmishers that you'd see in armies all over the world at the time, wearing little if any armor and carrying javelins, and a crescent-shaped wicker shield called a "pelte", which is where their name came from. They were fast and mobile, but had almost no staying power.

So the Thureophoroi formed a nice average between the two. They were armed with javelins and mobile enough to skirmish like Peltasts, but they had enough armor, a large shield, and the discipline to be able to withdraw and form a phalanx if necessary.

Because of their tactical flexibility, their role on the battlefield could be almost anything a general needed them to do. They served well to guard the vulnerable flanks of the inflexible phalangites, they could support the skirmishing peltasts, or flank and hit an opponent's sides or rear.