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The Hellenistic Age is a period after the death of Alexander the Great.

Stoicism is a Hellenistic philosophy founded by Zenon of Citium in Athens.

The primary difference is that Greek classical philosophy focused on metaphysics and ethics, exploring abstract concepts such as the nature of reality and the good life, while Hellenistic philosophy focused more on practical aspects of life, such as how to achieve happiness and tranquility through practices like Stoicism, Epicureanism, and Skepticism. Hellenistic philosophers were more concerned with how individuals could live a fulfilling life in the turbulent times after Alexander the Great's empire fell apart.

They were alike in that they were all heavily influenced by hundreds of years of Greek culture, art and philosophy. But Hellenic (that is, Greek) culure and Hellenistic cultures were different in that Hellenic culture kept its true, traditional forms while Hellenistic cultures in other countries were only an influence on local culture, art and philosophy but did not replace it. Each and every "Hellenistic" country was different from another by also staying faithful to much of its own traditions in philosophy and art.