When I hear the term “philosophical ethics” I think of several related and long-standing debates between multiple schools of thought. Deontology versus utilitarianism versus virtue ethics, intuitionism versus naturalism, cognitivism versus non-cognitivism, natural law versus positivism, et cetera, et cetera, et cetera. What unites philosophers working on moral problems is not a set of answers, but rather a set of questions and a methodology. This methodology is rational, non-authoritarian, and reflexive (that is, it questions its own assumptions).
Philosophers may be religious and think that God is central to ethics, they may think be secular and think that God is irrelevant to ethics, or they may even think that God is antithetical to ethics. Similarly, they may think that man is central, irrelevant, or antithetical to ethics. Unless the class you are in is using some special meaning of the term, I don’t think that “philosophical ethics” can be pigeonholed so easily.
This, in turn, suggests that we should not be too quick to pigeonhole the other terms either. Can a distinction be made on a similar methodological level for Christian moral theology and anthropological ethics? Perhaps it can. In fact, they might be considered fairly similar to philosophical ethics but with certain assumptions added that are not taken for granted by philosophers.
Christian moral theology might be seen as treating philosophical issues concerning morality under the assumptions that God exists, that Jesus was the messiah, and that Biblical commands act as a constraint on our practical theorizing. So it would have the task of finding a plausible moral theory that fits with those assumptions and constraints.
Anthropological ethics might be seen as concerned with descriptive, rather than normative issues. It takes the assumption that morality is a social construction that varies from culture to culture and investigates how and why those variations occur. It’s task under this interpretation would be to explain how all of these diverse practices are still recognizable as moral practices and how those practices affect societies in the short and long terms.
This is only one way of distinguishing between the terms, and it may not be what your teacher is looking for. Still, it seems to me more correct than saying that philosophical ethics centers on “man.”
Also, it’s unclear whether you are working with a two-way or three-way distinction. Are philosophical and anthropological ethics supposed to be different terms for the same thing or two distinct ways of approaching ethics? Obviously, I assumed the latter in my response above.