If you're talking about manual testing in the sense of "run down a long checklist", yeah that's different and automated tests are a better (although still not perfect) substitute for that kind of thing. But definitely still consider dogfooding to fall under "manual testing."
I don't think it fits under that at all, and I find that when people do see it that way it gets an entirely different treatment. "Manual testing" is an activity you do when you are thinking about how the product works. "Dogfooding" is a culture of using the product in order to achieve other tasks that you really wanted to get done.
