Proxy vs Reverse-proxy

The other day I was asked by a coworker the difference between a proxy and a reverse-proxy.
These are 2 types of servers that are largely used in front of an application server. Many companies and schools filter their internal network through proxies.
So I made this drawing, I think it should come handy to a lot of people.
Many people are familiar with the proxy server that they need to configure in their browser to access the internet. But few people are familiar with the reverse-proxy server.

To sum things up :
1) The proxy server’s main job is to cache pages so it serves them if the client asks them again.
2) The reverse-proxy server’s main job is to secure the servers as it takes the incoming requests from the internet and forwards them to the servers. Other jobs are : load balancing, filtering and also caching.

The reverse-proxy can be located in a demilitarized zone (DMZ), that is a very secured area, between 2 firewalls for instance.
One thing to remember :
if the firewall is removed, the client still can access the internet. If the proxy is removed, the client cannot access the internet.