These two schools of thought are different but sometimes so close that there is plenty of opportunity for cross pollination of ideas. For example Michel Humer's proof of objective morality uses the correspondence theory of knowledge. But it does not need to. As long as we have objective existence of the "dinge an sich" it is just as valid.
I.e there are moral judgments. They are true or not true.[law of excluded middle]. e,g, Stalin was a bad person of Stalin was a good person. This judgment corresponds with reality even if the character depends on the observer. Therefore moral judgments are objective .