I'm going to apply to graduate programs in both Statistics and Data Science. To me, Statistics, Data Science, and Machine Learning essentially refers to the same subject, but some universities are offering different programs. Still, it's rare for a program in Statistics to not mention DS/ML at all, and vice versa.
My undergraduate major is in Statistics, but my research experiences is mostly concerned with Machine Learning. When writing my Statement of Purpose, I'm struggle to justify why I'm applying to STAT programs with a background in DS/ML. Yeah, they are closely related, but wouldn't it be weird to say "Through my research experience in DS/ML, I developed an interest in STAT, so I'm applying to your STAT program"? The reason I'm applying to a STAT program instead of that in DS when both are offered is that the former is generally more academic, theoretical, and in-depth. (AFAIK there are no Ph.D. programs in DS, but it's hard to find a STAT Ph.D. whose research interest is not related to DS/ML.) I cannot say for now whether I'm going to work in academic or in industry, but I believe a sound theoretical background would be helpful in either case.
I don't think claiming STAT, DS, and ML are the same in the SOP would be a good idea either, as the Committee probably won't agree with me. How do I address the issue of terminologies, then?