Accuracy addresses the quality or state of being correct or precise, by other words technically addresses the degree to which the result of a measurement, calculation, or specification conforms to the correct value or a standard.
Correctness addresses the quality or state of being free from error; accuracy, by other words, there was evidence to support the correctness of the identification.
Correctness addresses the quality of being right in an opinion or judgement, by other words, he is trying to challenge the correctness of his criminal conviction.
Correctness addresses conformity to accepted social standards, by other words, the character was played with stuffy correctness.
It is same because correctly classified instances means the sum of TP and TN. Similarly, incorrectly classified instances means the sum of FP and FN. The total number of correctly instances divided by total number of instances gives the accuracy. In weka, % of correctly classified instances give the accuracy of the model. Cheers!