How does a proxy differ from a client

This might be a really bad question, but It would point out some helpful things.
also, what programs make out a proxy?

That is like comparing apples and oranges. They work in different ways. A proxy intercepts packets before they are sent to the server/client and manipulates them to achieve results. A client is the thing you play on. So in essence, a proxy can supplement a client (hacked or not).