Nylons work best with formal or fancy clothing. You will need to wear nylons or stockings, and nylons are more traditional than tights. It is an adornment to make your entire outfit look good. The color of nylons you wear should match your skirt or dress, and if you choose to wear skin-colored nylons, make sure that they blend with your skin. Nylons can also be worn at costume parties, and they are often worn with naughty costumes on Halloween.
Tights, on the other hand, are like a pair of pants, and you can wear them under a short skirt, dress, or shorts. Teenagers tend to wear them a lot for their versatility. Part of the reason that tights can serve many different purposes is that they are informal, and you can typically wear them with almost anything. Tights, like nylons, also come in many different colors, such as black and nude.