先把总结写在前面：通常两者皆为同义词，可通用。
如果懒惰看我这长篇答案，就请看上方总结。
简略总结网上查到的资料：
1. 同义词。
Garbage, trash, rubbish, or refuse is waste material that is discarded by humans, usually due to a perceived lack of utility. The term generally does not encompass bodily waste products, purely liquid or gaseous wastes, nor toxic waste products.
资料来源：Wikipedia: Garbage
2. 多义词
Rubbish:
Garbage:
资料来源：Cambridge: Rubbish, Cambridge: Garbage
Merriam Webster: Rubbish, Merriam Webster: Garbage
3. American English vs British English
Rubbish: British English (BrE) - British people throw away rubbish.
Garbage, trash: American English (AmE) – Americans throw away garbage and trash.
因为我国曾经是英国的殖民地，因此我国使用的是英式英语（British English）。
资料来源：Confusing words: rubbish, trash, garbage
10 Words Brits Use That Americans No Longer Do
Culture Clash: Trash vs. Rubbish
4. 垃圾分类
Garbage: Decomposable food waste or yard waste that is highly putrescible.
Rubbish: Dry material such as glass, paper, cloth, or wood that does not readily decompose.
资料来源：Refuse: waste management
我个人认为两者都差不多。
如果你怕被扣分，就用rubbish，但以（3）这个理由的话，其实美式英语和英式英语都差不多，老师通常不会扣分。（老师也不一定知道差别）
总而言之，你自己看着办呗。:P
扩充资料：Quora: What's the difference between rubbish and garbage?
Garbage 是垃圾的美式英语说法；rubbish 是英式英语垃圾的意思；trash 也是美式英语垃圾的意思，但是它也可以用来指不值得尊重的人；waste 是一个正式用语，指没有利用价值的东西或是浪费。
上网找就有了
