I have never seen a white cardamom (does not mean it does not exists). I am Indian and cardamom is a staple spice in my pantry. In general here are the guidelines for it's use atleast amongst Indian cooking. I know it's used in European cookies and pastries too but I would suspect Indian's use it more heavily than any others.
Green Cardamoms - Used in sweet dishes - Kulfi, Kheer (Indian rice pudding), Ras Malai, Masala Tea etc. Also used in Indian pilafs and curries as a whole spice for a unique aroma.
Black Cardamom - Very different in flavor and aroma than the green counterpart is mostly used in savory preparations - Biryani (an aromatic rice and meat dish) other pilafs and strong spiced gravies.
I would not recommend substituting one for another. In a pinch it's better to skip this spice then trying to compensate it with others. I know there are several so called substitutes but they are no where close in flavor and aroma to cardamom.
Green Cardamoms - Used in sweet dishes - Kulfi, Kheer (Indian rice pudding), Ras Malai, Masala Tea etc. Also used in Indian pilafs and curries as a whole spice for a unique aroma.
Black Cardamom - Very different in flavor and aroma than the green counterpart is mostly used in savory preparations - Biryani (an aromatic rice and meat dish) other pilafs and strong spiced gravies.
I would not recommend substituting one for another. In a pinch it's better to skip this spice then trying to compensate it with others. I know there are several so called substitutes but they are no where close in flavor and aroma to cardamom.