This is like asking what's the difference between she and her, or he and him. Not that it's not a legitimate question or anything but it's basic grammar. Look up "nominative" and "genetive" cases and compare, if you're truly interested. As for examples:

Я ничего не знаю - I don't know anything/I know nothing.
Я ничего тебе не скажу - I won't tell you anything/I will tell you nothing

Ничто не вечно - Nothing's eternal
Ничто не даётся бесплатно - Nothing comes without a price.