If you are into CV, first start with very simple static image recognition with AlexNet/VGG/Inception etc. in Keras, try to understand CNNs a bit (it's inspired by biological neurons, they can do simple things like direction detection, edge detection etc. and overlap each other's field of vision; if you look at computational photography, convolutions do something similar, so the idea is why not use a layer of multiple convolutions, then make a hierarchy of those convolutional layers, and let the optimization/learning part of Deep Learning during training figure out what exact convolutions does it need instead of force-feeding them by hand). Play with the ways to improve training (batch normalization, image augmentation etc.) Once you understand this, your mind would probably explode and then it's time to understand RNNs/LSTMs/GANs and have fun applying it on voice, natural language, generating art etc.
You'll have a blast for sure when you realize what you can now easily do! Have fun! ;-)
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.
Play with http://playground.tensorflow.org/ . Read today's https://news.ycombinator.com/item?id=14992865 about https://pair-code.github.io/deeplearnjs/ .