As many people have alluded to, I think the two are not the same thing. It seems to me that the difference between a programmer and an algorithmist is akin to the difference between a physicist and an engineer. One is focused on solving ideal problems, while the other has to know something about that, but ultimately the day to day work is much more about system building and finding a solution that works in the, much more fuzzy and dirty, real world.

There are many examples of this dichotomy. An architect has to know something about structural mechanics, but ultimately is more about finding a solution that fits within the constraints of structural mechanics that also does what it's supposed to in the real world.