n English, Eve’s etymology comes from the word evening, thus symbolises the impending darkness of the night. So too, Christian interpretations of Eve tend towards viewing her as a femme fatale who is responsible for Adam (the perfect male) falling into the darkness of sin.
The Jewish name Chavah literally means the mother of all life, which brings with it positive associations of nurturing, creativity, and the joy of living. When Chavah is united with her husband, Adam (humankind), the symbolic embodiment of the two represents human experience, for everyone whether they are male, female, or other.
Why the difference? Essentially, Christianity focuses on the physical while Judaism focuses on the metaphysical.