Forward vs Reverse Proxy: What's the Difference and When Should You Use Each? Alternatively: Forward

Forward vs reverse proxy clicked for me when I realized:

Forward: "I don’t want the internet to see *me*."
Reverse: "I don’t want users to see *my messy server setup*."

For reverse proxies, HAProxy is a beast for high-traffic sites.

Anyone use both in tandem? Like, forward for internal staff + reverse for public-facing apps?