In Elements of Statistical Learning, it distinguishes between "in-sample" and "training" error (Frankly, I found the chapter on errors to be very confusing, especially with how they use the different error terminology). Also see the question asked here: What is the difference between in sample error and training error, and intuition of optimism?
But it seems in a lot situations, when people refer to "in-sample" error in practice, they mean the training error, and the 2 are used interchangeably. Is this typically the case?