To help disambiguate terminology, as there is significant overlap of terms and various usages in the literature, I have summarized various moral terminology.
Generally moral discourse uses terms, down and dirty, and I will change as people request for any refinements or corrections:
Meta-ethical- Deals with the nature of morals themselves, what is a moral fact, what is a moral good or permissible as opposed to forbidden or impermissible, how do we acquire knowledge of moral facts, how do we use language to describe morality, etc.
Moral Cognitivism- Believes moral statements are truth-apt in that they are propositional and express a moral fact which is either True or False. Example: “Stealing is wrong” to a moral cognitivist is either a True or False statement.
Moral Non-cognitivism- Believes moral statements are not truth-apt in that they are not propositional and do not hold moral facts as true nor false. Example: “Stealing is wrong” is more akin to “Don’t steal!” and tells you what should or should not do as a moral imperative. (Moral Prescriptivism), or “Stealing. Boo Stealing!” (Emotivism).
Moral Realism- (Objective morality): Meta-ethical theory that acknowledges moral facts exist in the world, and at least one moral fact can be discovered independent of other minds existing, and is not contingent upon subjectivity of other moral agents. (A moral fact that is true regardless of opinion which we can independently discover on our own).
Moral Anti-realism- Meta-ethical theories, that include moral noncognitivism, that acknowledge moral facts exist in the world, but are true or false not because of some objective fact of the world that exists.
Subjective Morality- (Ethical subjectivism): A type of moral anti-realism that acknowledges moral facts exist, but are contingent upon the attitude of moral agents towards a moral proposition.
Moral Nihilism- (Error theory): A type of moral anti-realism that acknowledges moral facts exist, but are all false due to an instantiation error. (Example: “Stealing is Wrong” is false as there is no property that exists referred to as “wrongness” to instantiate “wrong” in the proposition to make it true, so it is in error and false.)
Moral Fictionalism- A type of moral error theory which allows moral statements to be expressed without assertoric force or ontological commitment. (Example: An actor saying a line of “Unicorns exist!”, or while telling of a story or joke.)
Moral Relativism- (Metaethical moral relativism): Moral judgements are not truth apt, but are contingent upon some non-objective fact of the world. (Example: Moral Cultural Relativism which holds moral facts are not absolute, but are only true or false in relationship or respect to a culture.)
Moral Relativism- (Normative ethical relativism): Moral principles that hold that morally permissible (right) or forbidden (wrong) actions are not universal, nor absolute, but are ethically subjective and prescribed within a specific moral framework.
Descriptive Moral Relativism- (Cultural Relativism): Describes morality that is based upon cultural norms and defining of moral goods, which is more an acknowledgment, not inherently an acceptance of the moral rule, that various cultures have specific views of morality specific to that culture and defined by that culture. (Example: Wearing of the hijab in Islamic cultures)
Divine Command Theory- A form of ethical subjectivism that morally right or wrong actions are based upon moral obligations to act in accordance to God’s commandments where the action of obeyance of the command is the moral good and the commands are absolute.
Moral Universalism- A meta-ethical position that holds some moral imperatives that exist that are true for all moral agents regardless of culture or time period. (Example: Human rights, or the minimizing of human suffering)
Moral Absolutism- A meta-ethical position that holds some moral actions are inherently moral or immoral regardless of societal beliefs, time period, cultural, or personal opinion. (Example: Divine Command Theory which holds that if God commands an action as moral, it is morally obligatory and absolute in that it is always a moral good to obey.)
Moral Consequentialism- Types of normative ethical theories which right or wrong actions are solely contingent upon the consequences of the action. (Example: The ends justify the means if a greater good is a result of one’s actions)
Moral Utilitarianism- A form of moral consequentialism that holds a moral action is right or wrong dependent upon the greater good or happiness, and subsequently the least amount of moral bad or displeasure, for the most amount of moral agents.
Rule Utilitarianism- A form of utilitarianism that prescribes normative actions as right or wrong based upon if the action is in accordance or confirms to a moral rule that results in the greatest good for the most amount of moral agents.
Act Utilitarianism- A form of utilitarianism that prescribes normative actions as right or wrong based upon the consequences of the act resulting in the greatest good for the most amount of moral agents.
Virtue Ethics- A normative form of moral theory which bases moral actions on personal characteristics of moral agents, vice upon consequences or rules which are to be obeyed.
Moral Deontology- Types of normative ethical theories which base right or wrong action upon moral duties to rules rather than by actions or consequence. (Example: The obeying of a law out of a moral duty is a moral good, not based upon the action itself, or based upon character, which makes it morally good action).