"Bitcoin exchange: you can buy and sell bitcoins, like in a regular exchange and you can use it as a regular wallet
Bitcoin wallet: you just keep your bitcoins. There as several of them but don't use blockchain.info's "
It's simple as it is. Bitcoin wallet is just like your drawer where you can put your commodity or lock but difference is bitcoin wallet is digital where you can keep ypur bitcoins and bitcoin exchange are bitcoin sites that handle the bitcoin trading
bitcoin exchanges are sites that handle all bitcoin exchanges, buy, sell, trading from fiat money to bitcoin as well as other cryptocurrencies and bitcoin wallet allow you to store bitcoin electronically