The demand for inferior goods increases with a decrease in income, whereas public goods are goods that can not be bought or sold.
When the consumer has an income he demands the goods according to his preferences. Goods consumed according to consumer preferences are called normal goods. Inferior goods are goods that replace these normal goods when the consumer's income decreases.
For example, if the consumer likes to eat meat and has an income of $ 100. If the consumer's income decreases for some reason to $ 50, the price of the meat gets too high for him. So he decides to consume sausages. The sausages are a inferior good as they were not the consumer's initial preference. If his income increases, he will return to eating meat.
Public goods are goods that are shared by all citizens and can not be bought or sold. For example, the playground of a square is a public good.
