Inferential statistics is about explaining an observed outcome in terms of its causing factors. Once we have explained it, then we can make predictions. Machine learning skips the explaining part and goes straight to making predictions, without attempting to understand the underlying process that led to the particular outcome. This would be the main difference, in my opinion.
By contrast, machine learning is primarily concerned with making the best prediction possible, even if that means sacrificing an understanding of the underlying mechanisms.
The Venn diagram of methods can have a fair degree of overlap.
Neither disposition is right or wrong, but they tend to have natural places where each makes more sense. If you’re trying to predict whether a picture is of a cat or a dog, you probably don’t care much about the constituent contribution of factors to one pictures dogness or catness. On the other hand, if you’re trying to predict traffic collisions based on characteristics of a roadway, you’re probably less concerned with the predicted number of crashes and more concerned with the relative contribution of a handful of independent variables.