Tensorflow vs Numpy math functions
Of course there is a real difference. Numpy works on arrays which can use highly optimized vectorized computations and it's doing pretty well on CPU whereas tensorflow's math functions are optimized for GPU where many matrix multiplications are much more important. So the question is where you want to use what. For CPU, I would just go with numpy whereas for GPU, it makes sense to use TF operations.
Is there any real difference between the math functions performed by numpy and tensorflow. For example, exponential function, or the max function? 
The only difference I noticed is that tensorflow takes input of tensors, and not numpy arrays.
Is this the only difference, and no difference in the results of the function, by value?