To the first point, I believe it's a spectrum.
To a practitioner, "better" can be defined along well-known dimensions. Suppose you know your data lies more or less on a straight line -- you could fit a NN model or a run a linear regression. In this scenario, linear regression would be the "better" choice for some widely-accepted measures of "better" (interpretability, computational efficiency, parsimony, regularizability, etc.).
One almost never chooses NN just for the sake of choosing NN... there are well-understood trade-offs.
For instance, it is widely known that NN's generally require a larger amount of data than classical/statistical algorithms for weights to converge -- mostly because it's fitting a more general function than most classical ML algorithms. (The reason NNs have begun to show the results they have (vs in the 1990s) isn't just because we have more compute than before or that the theory has advanced significantly; it's also because we have more a lot more data to fit the more general function with.)
To the second point, I can see the point, but I wonder if the semantic meaning of the term is eroded by being overly encompassing. We could say a calculator implements AI.