In your fig, I believe R is representing the coefficient of determination or the correlation coeeficient (https://www.mathworks.com/help/stats/coefficient-of-determination-r-squared.html).
Not only for NN, but any machine learning task, the whole dataset is first divided into training, validation, and test datasets. The model is trained and validated using methods such as cross validation, and the final model is assessed using the test set. In your fig, it looks like different models are compared using all four datasets showing different parameters fit different datasets better. For more, please check: https://www.mathworks.com/help/stats/model-building-and-assessment.html
