Aristotle and Apollodorus first write about Graeci, who seem to be the same people as Selle from Epirus. The name becomes known to Latins with the colonization of Italy from Greek settlers. While Greeks call themselves Hellenes, the Romans begin to call them Graeci, the name of the specific Greek colonists.
During the Roman era the name Hellenes is not used anymore. The Greeks, along with the rest of the people from the Roman provinces, call themselves Romans.
After the fall of the Western Roman State in 395 A.D. and the beginning of the Middle Ages in Western Europe the Latin term for the Greeks is used broadly. In Eastern Roman State a change takes place. While in general the citizens of the Byzantine Empire are called Romans, the Greeks assume the name Graeco to distinguish themselves from the rest of the Byzantines. After the schism the name Graeco meant orthodox and Latin meant Catholic. After a while the two terms assumed a national character as well.
After the independence of the modern Greek state from the Ottoman Empire the term Graeco or Greek was abandoned totally by the Greeks themselves. The new country was officially named Hellenic republic (or 'Hellas") and the people "Hellenes". The rest of the world calls them Greeks nevertheless and their country Greece.
Greeks is also a financial term for the set of measures derived from the Black-Scholes option pricing formula. The name is used because most of the parameters are denoted by Greek letters.