Morality: a system of beliefs based in individual motivation that dictate behaviors towards others and self. It is immoral to let bad deeds go unpunished.

Ethics: a system of beliefs based in group motivation that dictate the behaviors that would make the group run as smoothly as possible. It is unethical to sell term papers on the internet.

See also Immanuel Kant, John Stuart Mill, Aristotle

The division I have heard used in philosophy courses is that morality is a system that tells you how to act, and that ethics is the study of such systems.

I would take an existing system that tells you what is good or bad to do to be an Moral system, and the discussion of the theories of egoism, utilitarianism, duty ethics, virtue ethics, etc. to be about ethical systems.

This is one division that is used in some Ethics textbooks and at least one Ethics professor. It seems to be useful in some cases, but it is not standardized. (See Webster)

Let me try to be as exact and definitive as possible.

Ethics (Εθικη): From Greek, εθοσ ("ethos"), meaning "behaviour." Ethics is the philosophical study of human motivation and behaviour, and the ways in which psychology becomes personally normative.

Morality (Moralitas): From Latin, mos (pl. mores), meaning "custom" -- compare German Sitt. Morality is the philosophical study of interpersonal relations and their ethical ramifications.

Although both words are usually used in the "code of conduct" sense, this doesn't fit with the ways in which they can and have been studied. In former times, the study of ethics (including moral theory) subsumed the modern disciplines of psychology, psychiatry ("soul healing"), sociology, and even anthropology, religion, and law. Now that those studies have their own respective disciplines, ethics remains the forum for the critical analysis of these concepts -- "good" and "evil" (which are, strictly speaking, concepts from anthropology), "sin" (obviously a religious concept), "custom" (from sociology), "self," "identity," "happiness," (from psychology), "right" (from law), and so on. The study of ethics also involves the pursuit for the meanings of these concepts, rather than their definitions and applications, which is a matter for those other disciplines.

The study of morality is a subset of ethics dealing specifically with interpersonal relationships within a social framework. It has to do with the critical analysis of our roles in society, our "duties" and "rights" -- whether they exist, and if so what they are.

Neither system, ethics or morality, necessarily "tells" you how to act. The normative, prescriptive/proscriptive element -- the motivation -- is the whole focus of the study of ethics. It is part of the search for the meanings of these concepts and analyses. Friedrich Nietzsche, for example, said that we can create moral codes, and that our choice of morality cannot be objectively evaluated because values are personal.