The issues you're noting are definitional ones where standard, widely accepted meanings for each term have yet to be agreed upon -- different authors and practitioners use them differently. I think nearly everyone would agree that there is a high degree of overlap in their use. This is frequently the case during the emergence of relatively new fields. So, 10 or more years ago, data mining was widely considered to be a "bad" thing relative to theoretical, hypothesis-driven standards of research -- the "gold standard." Today, the stigma associated with data mining has been, for the most part, removed in common parlance.
Regrettably, these considerations can devolve into dogmatic, almost religious wars of turf where the contending definitions are a function and by-product of the discipline (the "turf") within which they originate. So, machine learning has largely developed within computer science departments, whose content overlaps with statistics, but it can be treated as a wholly separate discipline from statistics with a separate literature to command. Indeed, many ML practitioners will acknowledge that their exposure and experience evolved without any statistical considerations coming into play whatsoever. A good example of this is Chen and Xie's paper on "divide and conquer" algorithms for massive data -- http://dimacs.rutgers.edu/TechnicalReports/TechReports/2012/2012-01.pdf -- which notes that D&C approaches originated in ML and computer science but without any statistical consideration given to the accuracy of the approximating results. It took statisticians like Chen and Xie to ask and address the concern.
If it's helpful, one way that might reduce some of the confusion is to think of the relationships in Boolean terms. You could even develop a text mining algorithm to show the overlap in Venn diagrams based on term usage from a set of related documents. So, AI is a subset of ML. ML is a subset of computer science that overlaps with statistics. And statistics may (or may not) be a subset of mathematics. Big data is a technical consideration that is largely a computer science concern but it is also a subset of issues having to do with IT hardware, software and data architecture. But big data has impact on statistical analysis insofar as most 20th c approaches to statistical modeling have significant "in-memory" software limitations when the data gets too big. Data mining is an approach to exploratory research that is a subset of methodological and research design issues that overlaps with statistics as well as ML. And so on.
The bottom line is that the more you read on these topics, the closer you will get to arriving at your own understanding and definitions. You may have to get creative in this regard since you are unlikely to find crisp definitions in one, two or even a few sources.
