Well technically for Descriptive relativism yes. Only in saying that the rational relativist sees no moral absolute, but would say these things exist on the relative moral spectrum as beliefs within our population.
Pragmatists are probably more utilitarian when it comes to ethics but not metaethics. In that they apply a utilitarian principle toward ethics, looking at every moral view for utility to find pragmatic truth.
Pragmatic truth is probably best defined as that definition of good which is closest to objective by the empirical facts we have on hand. So at the individual level this can lead to different flavours of pragmatism.
Fundamentally the pragmatist believes in objective good, they just don’t believe it is possible to truly identify without us knowing all the facts of the universe. This also leads to a second feature of pragmatism (which I am oft prone to forgetting in my practice of it) is that it is not the individual that is being judged as moral or immoral, but the society individuals collectively create. Simply because one individual cannot have access to our entire collective knowledge as it is, let alone if we legitimately knew everything there was to know about the universe already.
Now we arrive at moral ecology which is the view that we have to manage our collective moral views as we would an ecosystem. There is some disagreement on moral ecology though, some think all views need to be represented and maintained while others (myself included) feel certain maladaptive and destructive moral views will always contribute to a negative moral judgement on humanity as a whole and don’t contribute to our survival, stability, security or moral progress.
The only valid criticism of Pragmatism I’ve come across really is that at times it conflates the distinction between normative and descriptive ethics, but no more than science conflates the distinction between empirical facts about the universe and the opinions on those facts. If anyone has other criticisms of pragmatism though I’d be willing to hear.
The one I’ve noticed myself reading this back; is that if the individual cannot know everything there is to know, then how would the pragmatist ever know if the society they are in is moral or not even if collectively we knew everything?
To put it simply though, pragmatism for the individual requires building ones own ethica pragmatica; A working theory of what good is, an obligation to hold true to that good with a moderate grip, so that one has the integrity to fight for it and yet isn’t so rigid that concrete evidence against their theory of good isn’t ignored.
Then you have adaptive pragmatism as a philosophy as opposed to pragmatic ethics (it is quite possible to be a philosophical pragmatist but not a moral one and vice versa) it’s only real difference between Pragmatism is that it requires a philosophy of science to be quantum accommodated, meaning a philosophy of science is incomplete without an attempt(A horrible, long and confusing attempt because of how probabilistic it is) at interpreting philosophy of quantum mechanics.
In conclusion, the answer to your question is Relativism is broad but pragmatism can be as broad or narrow as the individual pragmatist feels is justified.