A Data Analyst is distinct from a Systems Analyst or a Business Analyst. They may perform both systems and business analysis tasks, but their distinction comes from their understanding of statistics and how they apply that to other forms of analysis.
A ML specialist is not a Data Scientist. Did you successfully build and deploy an ML model to production? Great! That's still uncommon, despite the hype. However, that would land you in the former position. You can claim the latter once you've walked that model through the scientific method, complete with hypothesis verification and democratization of your methodology.
A BI Engineer and a Data Engineer are going to overlap a lot, but the former is going to lean more towards report development, where the latter will spend more time with ELTs/ETLs. As a data engineer, most of the report development that I do is to report on the state of data pipelines. BI BI, I like to call it.
A Big Data Engineer or Specialist is a subset of data engineers and architects angled towards the problems of big data. This distinction actually matters now, because I'm encountering data professionals these day who have never worked outside the cloud or with small enterprise datasets (unthinkable only half-a-decade ago.)
It doesn't help that lack of understanding often leads to misnomer positions, but anybody who has spent time in this field gets used to the subtle differences quickly.