What is the difference between concept learning and classification?
The objective is rather different.
For classification problems, we want to know: GIVEN X, WHAT WILL BE Y?
For concept-learning problems, we are asking: WHAT KIND OF X WILL GIVE US Y?

It may seem similar, but for classification problems, we may use a model that is unable to generalize and answer "WHAT KIND OF X WILL GIVE US Y" until you plug X into the model (e.g. K-nearest neighbor).

On the other hand, concept-learning problems, the main issue is to generalize and answer what can be X specifically.