Statistician - statistician generally work on the designing of SAP which consist of
analysis plan in the form of design, lay out or a sample table
where as programmer creates a table or report by looking at these sample tables.
They are apples and oranges. It is like cashier and the baker in a bakery. Even though both sell the cookie, both perform distinct roles with their distinct field expertise. Both have different window sight.
Programmer customizes the data gatherings to produce an output or report so that the viewer can see what is the behaviour of the data. Programmer can be indifferent to the key statistical details (as to what statistics produces what output). He is not authorized to make a calls on which statistical method to use (Cochran vs Cochran Matzel vs CochranMH to naem one) as he/she does not possess the statistical degree/expertise. But given the method programmer does know how to repor the output.
Statistician: Knows how to infer the conclusion from the data points. Statistics is not a straight math like 2+2=4. They have to infer if 2 apples and 2 oranges are just as sweet as 2 green vegetables and 2 sugarcanes. Given the size of study population (>30 or <30), the type of the data(numerical vs categorical), decide acceptable the typeI and II error rates based on what is gets looked at, which method to use to randomize subjects, the parameters involved, based on the study how many subjects are needed at least, paired t-test vs single t-test, z score vs t score, probabilities, what measures to measure to support the hypothesis. Programmer may not have the grasp of statistician's world.
Even though a statistician can go on and become programmer too just as a programmer can do MS in statistics and become statistician, both have different windows to work at if they have their key roles.