There is a lot of confusion about what is meant by “moral relativism” and “moral objectivism/realism”

“Subjective” and “objective” tell you about the source of the truth maker; i.e. what makes something true. Is it the beliefs of the subject (the person’s mind) that make it true, or is it an object in the external world? My belief that homemade vanilla ice cream is the best ice cream is what makes it true that homemade vanilla ice cream is the best ice cream for me. In contrast, the curvature of space-time is what makes gravity true – not just for me, but for everyone. Gravity is true regardless of what I believe about it.

As it applies to morality, moral relativism claims that what makes a moral claim true is simply that a subject believes it to be true. It doesn’t have to correspond to anything in the external world. Like preferences in ice cream, such moral truths are relative to the individual. These truths do not apply to everyone. In contrast, moral objectivism (moral realism) claims that what makes a moral claim true is that it corresponds to some moral reality in the external world. Like gravity, moral truths exist independent of our beliefs about them and applies to all people equally. There is no “your truth” and “my truth,” but only “the truth.”