So, the case 1 looks like a normal training process, and case 2 looks like overfitting: model learns your training dataset, but not learning general relationships in the input data (Its like instead of prepairing for the test, you memorized the answers)
Try to simplify your model, giving it less neurons, preventing it from memorising test data, and see if problem persists. Also, some graphs of loss and accuracies would be nice