I see differences between these two concepts. An ethic usually is related to a person's behavior, while a belief is internal and may not show itself outwardly. Check these definitions.
One's ethics and ones belief system have great similarities.
The discipline dealing with what is good and bad and with moral duty and obligation
Ones system of values.
This is much too vague for me to help.
what kind of ethic? work ethic? moral outlook? social ethic?
What kind of belief? Religious? The origin of the universe? The fundamental outlook on paper money vs Gold?
If you are looking for moral ethic (right and wrong) vs religious belief, my experience if you take a group of "similar" religious folks, say in a church, in a group of 100, you will have 100 different beliefs. It wouldn't surprise me to find that many divisions on right and wrong...such as gay marriage, divorce, child rearing, teaching sex in schools, abortion rights, and so on.
I suspect the correlation coefficent between the two is about .002