All of the material I'm reading on Proxy Firewalls, Content Inspection, Application Layer Firewalls & Web Application Firewalls indicates that they are inherently unique devices / applications. But the descriptions for each are so similar that it seems like there should be a broader relationship. I understand what each one does on it's own, but the line between them is really blurry.
For instance, doesn't a proxy firewall, which reads application layer data, inherently provide content inspection? Wouldn't that be the exact description of an application layer firewall?
Can anyone provide some real-world examples of when / why to implement each one of these devices vs any of the others?