All currently used deep learning algorithms are special cases of neural networks. The reason why this is called "deep" learning is that before 2006, no one knew how to efficiently train neural nets with more than 1 or 2 hidden layers. (Or could, because of computing power.) Thanks to a breakthrough by Dr Hinton, this is now the case.
But all models used are neural nets. It's just that a vast amount new algorithms for training them have been developed in the last years and people came up with new ideas on how to use them.
But it is all neural nets. And that's the whole beauty of it.