What you're referring to in movies is properly known as Artificial General Intelligence (AGI).

AI is correctly applied to systems that process in a "biologically similar" fashion. Basically something a human or "smart" animal could do. Things like object detection, natural language processing, facial recognition, etc, are things you can't program (there's more to facial recognition, but I'm simplifying for this discussion) and they need to be trained via a neural network. And that process is remarkably similar to how biological systems learn and work.

Machine learning, on the other hand, are processes that are intelligent but are not intrinsically "human". A good example is song recommendations. The more often you listen to a genre of music, the more likely you are to enjoy other songs in that genre. So a system can count the number of songs you listen to the most in a specific genre, and then recommend that genre more than others. Fairly straightforward to program and doesn't require any training, yet it gets better the more you use it.