From the perspective of a speaker of US English:

"Rubbish" is a word only used in UK English. It means "garbage," as in literal trash, "nonsense," as in words that don't make sense, and can even be used as an insult to call someone very, very bad.

"Garbage" is more commonly used to describe the things you throw away (in the US at least), and it can also be used to describe something as worthless or meaningless. "Garbage" is not very often used to describe people, but you can probably use "rubbish" to describe people, although it is quite rude.