Ancient Greek refers to the Athenian's classical language. The ancient Greek happens to be a language that has been in vogue during the Hellenistic, classic, and archaic periods. It can be traced to as far back as the second century BC. When it comes to Modern Greek, it is based basically on Demotic.
Another name that Modern Greek is known for is Neo-Hellenic or Romaic. Modern Greek actually became popular after the Byzantine Empire was declined in the year 1453. The ancient Greek is known to have a rich system of a vowel, while the Modern Greek has a simple system of only five vowels.
There was a clear distinction of length in consonants and vowels in the ancient Greek, while this has not been conserved in the Modern Greek. The operative mood, infinitive, dual number, and dative class that was prevalent in the ancient Greek have been given up in the Modern Greek.