Yeah, I find myself kinda annoyed at the term WAF, as it overloads the term "firewall". But your description is quite accurate. Whether you're doing your filtering with an expensive F5 Big-IP with its nifty glowy logo on the front bezel, an haproxy instance from some WAF-as-a-service vendor, or Nginx and some plugins running on a VM, any of those, done right, can serve in a WAF role.
I say that now, but I wish I understood that a few years ago, when faced with the WAF line item on an a WAF, promptly went "WTF is a WAF? googles No, we have a WAF." Could have saved myself some security audit pain.
On the flip side, I did manage to get some upgrade budget out of failing that battery of line items.
