The moral realism vs irrealism contrast is the most important contrast in metaethics, the study about what ethics is, such as whether morality is objective, subjective, emotion-based, rationality-based, changeable over time, etc.
Realism says morality is real in some sense, while irrealism says it isn't.
Infinity
For an example of such a contrast, we can consider the positions on infinity in mathematics. Realism would simply say that infinity exists, is an actual mathematical object, and there's a symbol of it, ω. Irrealism would claim that ω is just a convenient fiction, and merely stands for the endlessness of natural numbers.There are very fine-grained notions of realism vs irrealism in the study of infinity, too, used by expert set theorists. Most set theorists consider the first few infinities unproblematic, but as they climb up the ladder of infinities, they encounter more and more abstract infinities. They often draw a line somewhere and proclaim infinities beneath some line real and above unreal.
