Why is it needed to have both normal map and height map?

I have discovered the Bump node, that merges the effect of a height map and a normal map.
But since both give fake details, why to use 2 different kind of maps? If it was just to have 2 layers that you can control, well, why not just 2 normal maps?
I can’t understand why to use -also- a height map.

It has an history… Using height maps requires the calculation of derivatives and at least 3 calls to the texture. Normal maps represent those derivatives and you only need 1 call to the texture…

In the time (not so long ago) where every clock cycle was important, reducing a small bunch of calls in a function that is called for every pixel, was a need (and it still is).

Of course, height maps are easy to create; and for an artist, easier to manipulate and paint… but for real time rendering, normal maps give better performance.

Why both? Because you may need one, or the other, or even both.