Machine Learning vs Predictive Modeling

The above question seems to haunt most people who have been doing statistical predictive modeling before the term machine learning came into play. Nowadays it seems whoever have run a classification problem with any of the advanced algorithms like Neural Network, Support Vector Machine, etc. calls themselves a machine learning expert. But is this machine learning? We have this statistical/mathematical models from the early 60's . And the only reason not all of them was popular back then is because it was too advanced for the computing power available at those times.