What is the distinction between a clearinghouse and an exchange?

An exchange is a marketplace for trades, one that provides the match making engine and players that bring liquidity. When trades are executed and matched off, there needs to be a bank or other financial institution that will do the net settlement of funds, this is a clearing house.

A better way to understand is that exchanges usually require a clearing house to settle the funds associated with the trades. An exchange does not handle the clearing (or settlement) of funds by itself.

Any settlement bank that handles funds or net-off settlement on behalf of a client is essentially a clearing house.