What is the difference between np.sum and np.add.reduce?

Short answer: when the argument is a numpy array, np.sum ultimately calls add.reduce to do the work. The overhead of handling its argument and dispatching to add.reduce is why np.sum is slower.

Longer answer:
np.sum is defined in numpy/core/fromnumeric.py. In the definition of np.sum, you’ll
see that the work is passed on to _methods._sum. That function, in _methods.py, is simply:

def _sum(a, axis=None, dtype=None, out=None, keepdims=False):
    return um.add.reduce(a, axis=axis, dtype=dtype,
                            out=out, keepdims=keepdims)

um is the module where the add ufunc is defined.