Gold is a noun. It mainly refers to a type of metal, but it can also refer to the color associated with that metal, and is occasionally used figuratively as well.
Like all nouns, gold can function attributively, modifying a following noun. When it does, it usually has the "metal" meaning, often specifying the material the following noun is made of (gold watch, gold chains, gold bullion, gold foil, gold coin, gold dust) although other semantic relationships are possible (gold mine, gold market, gold rush), and the color meaning is possible as well, especially when the head noun is associated with color (gold paint, gold color, gold crayon).
Golden is a derived adjective. The -en suffix attaches to a noun and forms an adjective, which generally means either "made of 〜" or "resembling 〜", often figuratively.
Although the adjective can be used with the "made of gold" meaning (golden coins, golden eggs), it's most commonly used for the "resembling gold" meaning (golden age, Golden Gate, golden hair, golden color, Golden Retriever, golden years, golden rule, golden opportunity, golden girls).
When used in the sense "made of gold", the noun is a more likely choice. Gold spoon is more common than golden spoon when referring to an actual physical spoon made of gold.