I think the phrase "jiuzheng cuowu" means you are partly wrong, in contrast, "gaizheng cuowu" is used to express that you are totally wrong. But I think most of the time they are interchangable.
These two have one same character- zheng, it is the result or target of these two words. However, they have different emphasis since the "jiu" and "gai".
jiu:纠, it has a 纟.纟was writen as糸 in traditional chinese, it means hinged cords. Here is the link: http://dict.baidu.com/s?wd=%81L&tn=dict&dt=explain
gai:改，from the perspective of carapace-bone-script,it's left part-己,signifies a child on his or her knees, the right part signifies his or her parent stands by with a lash at hands. The whole part express that a parent taught the right way to do a thing if this child made some mistakes that a parent treats these mistakes as crucial problems. Thanks.
Below is a link of the carapace-bone-script or jia gu wen.Thanks