Difference between Machine Learning and Statistics

I run into this question a lot and I have heard statisticians say things like we all do machine learning because none of us actually runs a regression or classification by hand on paper. On the other hand - some computer scientist's I talk to say that when you use programmatic techniques to orchestrate an analytical flow compared to using a GUI in SAS / SPSS you are using machine learning. One more answer I have heard is that if you use algorithms like RandomForest, Deep Learning, GBM etc you are doing machine learning as compared to statistics. I think all the above are observations that are partly right. But, as a person trained in Computer Science and Statistics, I have a very specific test to split the two.