'Nonsense' is that something makes no sense. 'Rubbish' is something which is not worth reading or listening to. Sometimes we can use them to describe the same thing. If someone says something that you know is completely untrue, you could either say 'That's nonsense' or 'That's rubbish'. In other cases, they don't mean the same. For example, if you listen to an English song, and the words are 'Boop de doop, woop de doop' you would say that it was 'nonsense' (because it doesn't mean anything), but it isn't necessarily rubbish. 'Rubbish' means poor quality (trash, garbage), which might not be the case - it might be a good song that simply has 'nonsense' words. Similarly, you might describe a really badly-written book as 'rubbish'. It's not nonsense, however. It makes sense, but it's just bad. I hope that's clear. By the way, the word 'rubbish' is British English - Americans don't use it.