validation/training accuracy and overfitting
I'm not sure what you mean by 'intrinsic'.  

A higher training accuracy means you have found a model of the training data that doesn't describe the validation data equally well.  Because of this, any statistically significant difference in training-validation accuracy is due to overfitting.   Figuring out what 'statistically significant' means in this context is not totally trivial, unfortunately, but the general point still stands.