Well, AI is how we call machine learning these days. The deep neural networks we are using today are not exactly a new thing either (1960s), it is mostly just scaled up because we now have the hardware to do it.

AI is a vague term, ranging from simple game playing engines to humanlike sci-fi robots and godlike superintelligences. But now, most of the times, it just means machine learning.

It actually predates computing machines by about half a decade.

ML is a subset of ML