Socks: A garment that covers the foot and part of the leg usually made of cotton or wool and worn for warmth or for protection from abrasion from a shoe or boot.
Stocking: A close-fitting, usually knitted covering for the foot and leg, often made of sheer fabric as nylon or silk and rising high on the leg.
They are relatively close to each other.
Socks are meant to cover your feet (and sometimes ankle/lower calf) to absorb sweat/protect the feet.
Stockings are similar, but they go up to the knee/mid-thigh and are usually only worn by women.
(Bad explanation, could be wrong, but this is how i see the difference)
That is the british meaning of stockings, but less so in the US - by my answers here to date from what i am getting marked as correct vs. incorrect, duolingo in Esperanto is translating more into the US nuances of umdergarments (which is getting more confused than anything)