The difference is simply that golden is an adjective and gold is a noun and an adjective. "Golden" is not just for color; it can mean made of gold, or gold-colored or a wide range of favorable things, such as splendid, advantageous.
If I am describing an object I may say it is golden or gold-colored or even just gold. I tend to use gold as an adjective meaning that color mainly in informal conversation; otherwise I may use golden or gold-colored. Context matters a lot, and for that you simply have to get a feel for it. Golden, for example, is often used for plants. Gold is often used for clothing, curtains, colors of walls etc. Golden is often used for hair and when modifying other colors.
She came to the party wearing a beautiful gold dress.
She came to the party wearing a beautiful gold-colored dress.
For miles and miles, all you could see were golden fields of wheat! Her golden hair was braided neatly.
She painted her house a beautiful golden brown.