I'm having trouble understanding the definitions of these roles. I see the chart, but the terms are all vague to me. What does a data scientist do that a mathematician or scientist doesn't do, and what does a scientific programmer do that a data scientist doesn't do?

My impression was that "data scientist" was a colloquialism for "statistician that knows how to program." Is a scientific programmer just a programmer that knows some statistics? Why is the direction important? The author says he/she feels that a programmer that knows statistics can make "more robust software" than the other way around, but what exactly does that mean? Do they mean "doesn't crash as much", or do they mean "gives the right answer more often?"