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The acronyms aren't changing, machine learning, deep learning, and neural networks have been around for 50 years. It's only recently that code libraries like TensorFlow have abstracted away a lot of the math to the point that it's relatively accessible to normal people that can write code.

Deep learning is a subset of machine learning that utilizes more than one layer of neural networks. So these terminologies just refer to different parts of the same process. The 'process' is just tweaking a program to progressively make more accurate yes or no assumptions about a set of statistics that you give it. That's my best shot at it, hope it makes sense.