Does machine learning (ML) use artificial intelligence (AI) or does AI use ML?

AI is a poorly defined term and that leads to many confusions. In my opinion, ML is a subset of AI.
In a nutshell, AI is when a machine or a program simulates human behaviour. Ideally, AI should allow the machine to think without direct human intervention. The ML systems should be able to automatically learn and improve by processing a large amount of data without explicitly being programmed to do so.

An example of an ML is a factory that has sensors that transmit data to an ML system that processes it and detects anomalies that humans can then address. The ML goal is to learn from the data and provide an output that someone can act upon.
The goal of AI is to produce a system that is intelligent and can perform tasks like a human or solve complex problems like a human.

Machine learning and AI are interrelated. To understand the correlation between these aspects, we need to understand the human equivalent of those technologies. 
Intelligence and emotions are two human elements. Despite the fact that we call it artificial intelligence, we are actually defining it as the intelligence humans would normally display. 
Things like situation handling, decision-making ability, etc. are coming under "Human Intelligence". These are different for a different person and are totally dependent on the experience and exposure of the human being. The "experience and exposure" are the equivalent of machine learning. This is the reason we train our ML model to give them exposure and experience, which they can utilize for intelligent decision making aka Artificial Intelligence.
Interestingly, by training the models with a lot and a lot of data we are actually standardizing the decision-making capability of machines to perfection, things which cannot be certainly told for humans. This is the power of AI and ML, now you call AI under ML or ML under AI, I am living it on you to decide. :)

When I was in college, I took an AI class.  This was many years ago.  There were a few different types of AI that we explored but we spent most of our time building expert systems.  No one would call that AI now.  

There is that it quits being called AI as soon as it works.

Advanced analytics, rules engines, NPC engines, chess games, etc. were all considered AI most are no long. 

ML is a tool.  It is one of may tools out there that are under the domain of AI.  It is the most popular tool at the moment but something else will come along.  But AI will still be the thing being pursued.

Beyond that I think the debate is if an AI is a test of general intelligence (Turing) or anything that replace human intelligence (my old expert system).  I lean towards the later but I tend to use it as an adjective.  I do sometime slip though, and think of it as a noun, then I'm in the Realm of Asimov and the general intelligence.

While most people associate AI with deep neural networks, the overall goal in either is to find and exploit patterns within existing data. And so for most practitioners in my field (drug discovery), we often equate the two.

For whatever reason, people today are enamored with AI and think that what they're seeing is AI. But there aren't many people who've truly solved it. There is much more machine learning going on than there is true AI. We still don't have fully automated data centers but we should—I've had vendors pitch that to me for the last 10 years and nobody has ever delivered on it. I think we have bits and pieces of it. 

I used to own a Tesla but have since moved to another electric vehicle because, among other things, I learned that the car was actually ML and not AI. When it was driving itself mindlessly towards the concrete barrier, the sensors were going off but the car was not doing anything; I realized there is no way it’s actually doing AI. It's doing pattern recognition. It hadn't seen this problem before, so it didn't know what to do. After I swerved and slammed on the brakes, then it knew, but that still didn't prevent it from going into a different concrete barrier later on. I applaud them for pushing the envelope, but they have highlighted how difficult a problem AI is.