Let us characterize metaphysical realism as the view that there is exactly one true and complete description of the world, and let us characterize conceptual relativity as the denial of that claim.
These two opposing views, at least in name, come from Putnam's discussions in, among other places, the books cited at the end of this post, and have since been discussed by many philosophers. It is not clear to me whether Putnam ever took the characterizations I have given as full characterizations, but they have certainly been for him at least part of what is involved in the two views.
Putnam used different characterizations at different times, and plenty of people have worked at sorting that out a bit. I'm not getting into any of that. I just want to stipulate the above characterizations, and briefly indicate how the doctrine of semantic granularity can dissolve the appearance of a hard- or impossible-to-resolve philosophical disagreement here.
It can do this as follows. If a complete description of a domain D is a set of propositions such that every proposition which says something true about D means the same as one of the propositions in the set (or a conjunction of them), then whether we say a description of the world is complete depends on the granularity we are operating at. Conceptual relativity may hold at a certain granularity, but once you make the granularity finer, it may collapse into metaphysical realism.
Seen in this way, where one claim, conceptual relativism, holds at one granularity or set thereof and the other, metaphysical realism, holds at another (finer) one or set thereof, they are not inconsistent with each other, and each has its own point.
Conceptual relativity as it were emphasizes the possibility of attaining the same or similar goals by different cognitive and linguistic means. Metaphysical realism on the oher hand emphasizes what we might call the sovereignty, the special individuality, of the different ways of doing things.
Putnam, Hilary (1981). Reason, Truth and History, Cambridge: Cambridge University Press.
Putnam, Hilary (1985). Realism and Reason, volume 3 of Philosophical Papers, Cambridge: Cambridge University Press.
Putnam, Hilary (1990). Realism with a Human Face, Cambridge, MA: Harvard University Press.
Not to mention the innumerable writings by others dealing with Putnam's philosophy.