AUC and Accuracy

AUC and Accuracy are fairly different things. AUC applies to binary classifiers that have some notion of a decision threshold internally. For example logistic regression returns positive/negative depending on whether the logistic function is greater/smaller than a threshold, usually 0.5 by default. When you choose your threshold, you have a classifier. You have to choose one.

For a given choice of threshold, you can compute accuracy, which is the proportion of true positives and negatives in the whole data set.

AUC measures how true positive rate (recall) and false-positive rate trade-off, so in that sense it is already measuring something else. More importantly, AUC is not a function of threshold. It is an evaluation of the classifier as the threshold varies over all possible values. It is in a sense a broader metric, testing the quality of the internal value that the classifier generates and then compares to a threshold. It is not testing the quality of a particular choice of threshold.