No, there’s no cage match between the two terms, but there is a distinction: Although the words can be considered synonyms, morals are beliefs based on practices or teachings regarding how people conduct themselves in personal relationships and in society, while ethics refers to a set or system of principles, or a philosophy or theory behind them. (Principles, however, is itself is a synonym for morals.) One lives according to one’s morals but adheres to one’s ethics while doing so. Morals are the tools by which one lives, and ethics constitute the manual that codifies them.
Moral is most familiar to most people in the sense of “lesson,” as in the moral of the story in a fable or a parable, or as an adjective, as in “Moral Majority” or “moral quandary.” The quality of having qualities consistent with high ethics is referred to as morality, and to teach morals is to moralize (though this term has a negative connotation suggesting self-righteousness). To demoralize is not to do the opposite of moralizing; it denotes erosion not of morals but of morale.
Morale, though it looks related to moral, might seem unconnected, but it is actually a synonym for morals, though that sense is rarely applied. Even in its more common meaning, referring to one’s psychological state regarding one’s condition or a group’s esprit de corps (translation: “spirit of the body”), it fundamentally means an adherence to a belief system: A person’s morale is based on the degree to which the moral standards evinced in their external environment are consistent with their ideals.
Two other words related to ethics and morals are ethos and mores. Ethos refers to a system of moral behavior, and mores denotes moral customs — the same intellectual and practical distinction present in the two primary terms.
A synonym for morals is scruples, although the etymology, interestingly, approaches the issue from the other direction: The Latin precursor, scrupulus, means “anxiety” or “pang of conscience,” but the literal meaning is “small, sharp, stone”; a scruple, in effect, is something that unpleasantly reminds you to be pleasant.
And what’s the difference between amoral and immoral? It’s significant: Immoral (“not moral”) implies a conscious decision to act against societal norms, whereas amoral (“without morals”) suggests that the person in question operates without any regard to them at all.