You seem to be suggesting that "relativism" means no punishment. I didn't think this was an accurate assumption, so I looked it up in the most authoritative resource in the world. It turns out that there are different categories of moral relativism:
Moral relativism may be any of several philosophical positions concerned with the differences in moral judgments across different people and cultures. Descriptive moral relativism holds only that some people do in fact disagree about what is moral; meta-ethical moral relativism holds that in such disagreements, nobody is objectively right or wrong; and normative moral relativism holds that because nobody is right or wrong, we ought to tolerate the behavior of others even when we disagree about the morality of it.
Link. Under these definitions, what you are describing is "normative moral relativism". Taken to its extreme, this philosophy would seem to prohibit enforcement of criminal laws. I don't believe in this.
I guess I'm a "meta-ethical moral relativist". Nothing is objectively right or wrong, but that doesn't mean nothing is right or wrong, nor does it mean we can't punish people for doing wrong. The tricky part is constructing a set of laws that delineate what is right and what is wrong.