What is the difference between data scientist and statistician? Have you ever seen data scientist, like with a PhD? Have you ever seen statistician with PhD like https://statistics.wharton.upenn.edu/programs/phd/ ?
[1] http://www.zipfianacademy.com/
Edit: Cabinpark is right and I should clarify. Statisticians typically don't have the proper computer science fundamentals to be able to deal with the programming required to run the right experiments. They may have an understanding of the distributions, t tests, ... but may not be able to use the tools out there that the broad field of data science requires.
When I hear the term data scientist, I assume that the person has extensive training and background in statistics and mathematical modeling. I work with large data sets all the time as a scientist and can run all the standard statistical tests but I would hardly consider myself a data scientist.
I think the problem with a lot of data science teams out there today is the hiring. Not a lot of people understand what the role of a data scientist should be and they expect these people who can do hadoop end to end, extensive CS skills, know all of the latest advanced machine learning algorithms, and know stats like the back of their hand.
Many employers will not need or use that full pipeline, and if they do, they are probably capable of hiring hadoop engineers as well as more traditional analysts who are deeper in the math with the models.
That analyst is someone with a specialized background and some form of training in scientific computing. This does not need to be a full blown masters/phd.
Realistically, you can get away with having a decent programming background, a clue about the landscape of the machine learning algorithms, and enough statistics to know when you're going down a rabbit hole with respect to research.
I think it more comes down to having the right mindset with problem solving. Much of this is also going to be domain specific.
The term data science is ambiguous at best, as it is a new field. I think over the next few years we'll come to see more specialized roles over time that will help clarify the sandbox that is data science vs data engineering among other disciplines.
I think a subset of that program would be rightly called data scientists. There is significant overlap, but statisticians are stronger in mathematical theory while data scientists are stronger in programming and computation.
At least that's how I see it. It's not particularly well defined at the moment, and a lot of people throw these words around because they're new and fun.