The Cretan Civilization:
The Cretans were a very technologically advanced culture. They lived on a very rocky island, and so had to develop fine ships in order to trade for what they could not get locally. This idea of trade carried over to the Greeks.
The Hellenic Civilization:
The Greek-speaking people did not call themselves Greeks or Grecians. They called themselves the Hellenes and their country Hellas. The Greeks of today still refer to their country as Hellas. Greek is the Latin name for the Hellenic people. The Hellenes were nomadic tribes, including the Dorians and the Ionians, who invaded what is now known as Greece from their lands to the north. Although more primitive in their technology, the Hellenes conquered many other early Aegean civilizations, including the Cretans, and took over their lands. They intermarried with the conquerees, and made use of their great technologies in order to farm the rugged mountains of mainland Greece.
In mythology there were four branches of the Hellenic peoples: The Achaeans, the Aeolians, the Dorians, and the Ionians. These names come from the four mythological sons of Hellen, the son of Deucalion.
Homer refered to the Greeks as Achaeans in the Illiad and Odyssey.