Out of bag error:

A) Is the estimation of how "typical" the dataset at hand is. Does it represent the true underlying population distribution(s) well or it is highly unusual and biased?

B) is the training set error, obtained while performing tree bagging: the OOB is calculated by predicting each given observation yiby averaging predictions of all the models trained on the bootstrapped datasets (i.e. it is a proper bagged model prediction).

C) is the estimation of the test set error, obtained while performing tree bagging: the OOB is calculated by predicting each given observation yiby averaging predictions of all the models trained on the bootstrapped datasets that do not contain yi(i.e. it is a proper bagged model prediction, just with smaller "bag" of trees).

D) is the estimation of the test set error, obtainedusing a "classical" bootstrap or cross-validation procedure: we take a subset Diof the original data (through bootstrap or through random subsetting without replacement as in K-fold crossval), then we perform the full bagging/random forest construction just on Di(multiple booststraps, build a tree on each bootstrapped version of the data), then we use the average of the predictions of all the models we just constructed to predict on the data points that are not in Di. Then we repeat the whole procedure multiple times (i.e. select new Diagain, perform bagging/random forest on just that subset of data, predict test set outcomes, etc).