What is the difference between cross-entropy and log loss error? The formulae for both seem to be very similar.
They are essentially the same; usually, we use the term log loss for binary classification problems, and the more general cross-entropy (loss) for the general case of multi-class classification, but even this distinction is not consistent, and you'll often find the terms used interchangeably as synonyms.
From the Wikipedia entry for cross-entropy:
The logistic loss is sometimes called cross-entropy loss. It is also known as log loss
From the fast.ai wiki entry on log loss:
Log loss and cross-entropy are slightly different depending on the context, but in machine learning when calculating error rates between 0 and 1 they resolve to the same thing.
From the ML Cheatsheet:
Cross-entropy loss, or log loss, measures the performance of a classification model whose output is a probability value between 0 and 1.