As far as the correct usage of the term "moral relativism" goes, it's used today in basically the same way. Those who believe in a higher standard of ethics and morality use this term to describe others who don't aspire to that same standard.
To be more precise, the term is
misused by idiots to describe people with a different morality from them.
But the proper meaning of "moral relativist" is not "someone with a different moral standard from me" or even "someone with a lower moral standard from me", but "someone who thinks that the concept that some moral standards can be 'higher' or 'lower' than others has no
objective meaning."
To take an example, Moses and Hammurabi alike would doubtless be shocked at our moral laxity in not putting adulteresses to death. But it would be incorrect for them to call us "moral relativists" on that account --- because we refrain from doing so because we think it would be wrong to do so.
Actually wrong. If we were asked: "Why is it not your custom to kill adulteresses?", we would not simply reply: "
Because it
is our
custom not to kill adulteresses".