Wikipedia
The Graecians (Graeki, Graii, Graeci; Greek Γραίοι, Γραίκοι), were an Ancient Greek tribe. Their name is the origin of the Latin (and English) Name of the Greeks as a whole.
It is likely that the Graecians were among the first to colonize Italy (i.e. Magna Graecia) in the 8th century BC, so that they were the first Greeks with whom the Latins came into contact, who consequently adopted the name of Graeci by synecdoche as the name of the Hellenes.
Aristotle records that the Graecians were the inhabitants of Hellas (a region within Thessaly), who were also known as 'Hellenes'. In later times Graecians settled in the city of Dodoni in Epirus from where they went on to establish colonies in southern Italy. In Italy they founded the new Hellenic colony Naples (Νέα Πόλις "New City").