The Wikipedia article of Chiral symmetry doesn't differentiate the two terms "chiral symmetry" and "chirality", hence confusing me. Are they the same?
Yes, chiral comes from the Greek word χέρι for hand. But in a way chirality and chiral symmetry are opposites: Both your hands together are an object with chiral symmetry because "mirror image of two hands" looks the same as "two hands" - though the reflection interchanges the hands, so to speak. On the other, erm, hand, a single hand (your right hand, say) shows the property of chirality because its mirror image looks different (like a left hand).