If you look deep enough they are not exclusive. From the deeplearning book: "Many authors use the term “cross-entropy” to identify specifically the negative log

If you look deep enough they are not exclusive. From the deeplearning book: "Many authors use the term “cross-entropy” to identify specifically the negative log-likelihood of a Bernoulli or softmax distribution, but that is a misnomer. Any loss consisting of a negative log-likelihood is a cross- entropy between the empirical distribution defined by the training set and the probability distribution defined by model. For example, mean squared error is the cross-entropy between the empirical distribution and a Gaussian model" https://stats.stackexchange.com/questions/288451/why-is-mean-squared-error-the-cross-entropy-between-the-empirical-distribution-a https://stats.stackexchange.com/questions/288451/why-is-mean...