The "moral sense" plays a central role in the study of "Humanities". There is a bit of ambiguity in the question as both terms are very broad, yet it's clear that morality is a core element. It's just that the same can be said of cultural anthropology, religion, sociology, social psychology, clinical psychology, judicial systems, politics and ethics...and so on.
Morality is everything. its the start of self awareness. It plays as a building block for society , much like an atom to a molecule. If you shape someones morals as a child you can charge them as a person(how they act, what they like etc. ). things that shape your morals are parents, schools , friends, how the people around you act. Religion is what really shapes our society's morals(even if there wrong). for example the 10 commandants. Most of the western world is shape by the 10 commends as much as we don't like to think. Without the 10 commandments morals( or a system of wrong or right) would have to be shaped by something else like a ruler or laws( not base on christ).
I am wanting to refine this idea. please find whole is any.