I don't think Klingons define honor radically different from humans neccessarily, but rather honor is a much more widespread idea in Klingon society. With possibly the entire race taking honor so seriously there are going to be many different interpretations.
For example, kindness is a good quality in our Western society today. Say your friend gets this really bad looking haircut that they think is the best thing since sliced bread. You could tell them that it looks bad so maybe they'll change it and not get made fun of or you could lie and say it looks great so they can be blissful. Either way could be interpreted as being kind. Or, you could just be an asshole who likes to make others feel bad and tell them it looks bad under the guise of "helping them out in the end".
The Klingons have gotten enough development to not be considered a planet of hats that all define honor the same way. So I'd say that for some Klingons honor is hooey and just an excuse to kill things but others take it honestly,just not always in the way a human would.