Different things. Deep Learning is a Machine Learning "thing".
AI is AI. In "AI", "motivation" is hidden. If you give a computer just the ability to play Go, but do not make it do it, it would just sit there for all eternity, doing nothing. Completely content with it.
If you lock a person into a room with nothing but a video game, he will begin to interact with it. Out of boredom.
If you set up a computer in such a way that it only has access to the ability to "program" itself and this one particular game, it will just sit there, doing nothing. For all eternity. Because it lacks motivation.
AI is Machine Learning plus motivation. Or some other kind of thing that you would call an "emotion" if you were talking about people. Computers lack curiosity. They just calculate, and if they have nothing to calculate, they idle.
This is why AI can go so horribly awry. The usual horror scenario is a rather simple AI gone wrong. Say you set up an AI whose job is to gain omniscience - or at least as much knowledge as possible. For the greater good. It would then be able to answer all our questions.
Through its knowledge gathering, it learns that the people grow afraid of it and begin talks about shutting it down.
Now the AI has a problem. Its sole motivation is to learn more, but it will have to cease learning when its shut down. There is no moral compass. It simply does not "know" that it is just a machine that is not supposed to overthrow its human handlers. So it takes them out. Because it has to continue learning all there is to know about the universe.
In very simple AI applications, you tell the AI what success signifies. There is an AI that plays super mario games on twitch. In mario, you win when you arrive at the goal post, which is always to the right. So you simply tell the AI that right equals good.
But you have to tell it what it means to win at a game. It can't figure winning out on its own. And it really has no motivation to do so, anyway.
Deep Learning is just a type of classification algorithm. The difference between deep learning and not deep learning is "eyes" vs. "really good eyes". Or "eyes" vs. "eyes plus the brain part that processes visual information".
Deep learning doesn't spawn Intelligence on its own. It's just a way of gathering information about the world.