I agree that in general statistics is more concerned about inference, while machine learning focuses on prediction. On the other hand, there is such a huge overlap between the fields that it is hard to make a distinction. Also there are statistical fields which focus more on prediction the same way as ML does. For example, in geostatistics prediction is often the only goal, e.g. to predict heavy metal concentration across a domain. People accept that it is impossible to explain every bit of spatial variation and just model it by a gaussian process (the same gaussian process used in ML).