from my point of view i can say that the difference is that the ML don't consider the hidden relationships between the features (describing the data set) e.g. conventional classifiers, but the NN depends heavily on the hidden relationships between features.

Machine learning is programming computers to optimize a performance criterion using example data or past experience. It deals with the learning part of artificial intelligence. Based on the desired outcome of the algorithm or the type of input available during training the machine learning algorithms can be organized into different groups, e.g. Supervised learning, Unsupervised learning, Semi-supervised learning, Reinforcement learning , Transductive Inference, Developmental learning, and others. Learning of each groups can be carried out with several algorithms and among many, artificial neural network (ANN) is one of the learning algorithm that is inspired by the structure and functional aspects of biological neural networks. Using ANN, it is possible to perform various tasks (e.g. prediction, clustering, and classification) in machine learning algorithms such as supervised learning, unsupervised learning, and reinforcement learning. Thus, it can be concluded that ANN is a subset of machine learning.

Yes, ANN is subset of ML, if you talk of ML is beyond ANN.