There are multiple discussions on web describing details about them. But to put it plainly for you:
Deep Learning is a subset of machine learning. It's the machine learning part that deals with neural networks.
So now, syllabus wise:
Deep learning syllabus would be part of machine learning syllabus. Quantity wise, Machine learning would be much more on an average covering other algorithms too.
If you plan to study or take a course of deep learning, it might go a little more in depth compared to what would be covered if you just do Machine learning cource/book (which would not go too deep into Neural Networks)
For more details on them, seems you have already Googled it off!