A statistical model is a formalization of relationships between variables in the form of mathematical equations, based on programmed instructions, we can find regression analysis and linear models, statistical inference, etc.
Machine learning is a subfield of computer science and artificial intelligence which deals with building systems that can learn from data, instead of explicitly programmed instructions, where we can find for example: Decision tree, Association rule, Artificial neural network, Inductive logic programming, Support vector machines, Cluster analysis, etc.