The word "morality" is used in several distinct ways in philosophical literature. One feature of this is time period of authorship. The English word "morality" is a cognate of the Latin word moralis which Cicero used to translate the Greek ethikos. Thus, on a certain level, the pair should have the same meaning. Sometimes, this does occur.
There are other cognate terms as well, mores and ethos refer to the practices of a particular culture or people.
In Hegel, the terms Moralität and Sittlichkeit refer to the goal of a universal morality (potentially identified with Kant) and the values that grow out of a particular people. Moralität commits the sin of being unmediated insofar as it creates an ought outside of the domain of Spirit. (see here). For Hegel, the key image is Antigone -- with the challenge of the requirements of the state as set against the Sitten of the family. For Hegel, the solution is a morality that is also ethics.
Contemporary philosophers do not necessarily follow Hegel. In much contemporary work, "moral philosophy" is an equivalent to "ethics" which is understood to be the discipline in which we study questions of action and right or wrong (sometimes called "axiology" but this is a word I see little written in actual philosophy papers).
Whence "morality"? Morality also seems to take on a popular meaning as the morality of society. Thus, the link to Christian in some uses. But in all honesty, I think this is kind of boogeyman usage, where we need a whipping boy to distinguish genuinely thought through moral philosophy from common practice.
An implicit claim in the use of the word "morality" is linked to the Hegelian usage above in that the term "morality" often implies a universal viewpoint whereas "ethics" does not carry this implication.
For instance, Roger Ames would write Confucian Role Ethics rather than Confucian Role Morality.
Similarly, we call it professional ethics rather than professional morality.
But we have the text Prospects for a Common Morality.
Thus, I would say in contemporary philosophy that "ethics" is generally a safer word choice than "morality."
While the above is broadly based on my experience with the literature, here are a few references to help with respect to Kant and Hegel on these terms:
Jon Stewart Kierkegaard's Relation to Hegel Reconsidered (Cambridge University Press, 2003), p. 311. He cites Alfred Elsigan "Zum Begriff der Moralität in Hegels Rechtsphilosophie," Wiener Jahrbuch für Philosophie 1972, p. 88 and Hegel's own *Philosophy of Right.