They are synonyms with the meaning of "the way of life, the experiences someone has,the activity in the areas of life". But they have some other separate meanings: Βίος can also mean "biography". Ζωή is more like "life" ie not being lifeless. So, Βίοι επιφανών ανδρών=Life/Biography of prominent men, Περιπετειώδης βίος/ζωή=adventurous life, Συζυγικός βίος/Συζυγική ζωή=Married life, χιλιάδες ζωές χάθηκαν=thousands of lifes were lost. Η ζωή σε άλλους πλανήτες=Life on other planets. In the above examples, where I use only one of them, the other cannot be used.
Reminds me of the Russian word "жизнь" (life). I wonder if they have a common PIE root.
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HOW TO GET THE GREEK KEYBOARD AND MORE HELP FOR NEW LEARNERS :
There you will find a lot of links to help you learn the Greek letters, how to add accents, where to find the letters on the keyboard, how to pronounce the letters etc.etc.
Η • ζωή: zoí /zoˈi/ •
From Ancient Greek: ζωή: zōḗ: life, lifetime • Zoë • From Ancient Greek: ζωή ( Zōḗ, Life ), a calque of the Biblical Hebrew: name חַוָּה: khavá - alive f Eve • חַי: kháy - To Live
ζωή: zoí /zoˈi/ life, lifetime • ζώο: zóo - mammal, animal, beast, creature • Ancient Greek: ζῷον: zôion - animal, beast ) • From Proto-Hellenic: ďṓyyon: animal, creature, beast • from Pre-Hellenic gʷyōwyon, from Proto-Indo-European: gʷyeh₃w-y-om, from gʷíh₃weti: to live • Cognate with βίος ( bíos: life )