Moral Relativism is very very odd and has probably come from practical anthropology rather than actual philosophy. I think moral relativism works as a description of the way people in our culture act. But if you're talking about a well thought through philosophical position a better comparison is between "Moral Absolutism" and "Moral Nihilism" where nihilism is simply that there are no moral propositions that are true or false. (Also known as Moral Skepticism which is similar)
Unfortunately my answer to your question was deemed "too long" by Yahoo!!! So I've had to post it on my blog instead. You can find it here: http://thevr.net/2013/09/20/moral-absolutism-vs-moral-relativism/
Feel free to ask specific questions in the comment section of that blog.
The final summary paragraph I wrote was:
In summary. Moral relativism I don't think is a defensible philosophical position (But look into that stanford article in my sources yourself, especially read the top paragraph). The interesting philosophical discussion is between moral absolutism and moral nihilism. However philosophically this question is so hard that pragmatically we may want to act like moral agnostics. If we have this attitude a moral relativistic stance will probably be the safest. If a whole group of people all think murder is fine and I think it's not, then I'll give them the benefit of the doubt until I get really good evidence to the contrary.
http://plato.stanford.edu/entries/moral-relativism/ - Really good.
My own thoughts and observations particularly after reading a bunch of Brendan O Neil's articles on spiked online and particularly the Chapter on Nietzsche in Bertrand Russel's "History of Western Philosophy"