I think of "programming" in "dynamic programming" the exact same way I think of it in "linear programming", "integer programming" and "constraint programming": it's probably some kind of software development that some computer scientists came up once and that I don't need to think about, because my normal programming has worked out pretty well so far

(Except, well, I guess I understand what "dynamic programming" is more than I understand what the other forms of programming you mention is; "dynamic programming" is solving certain classes of recursive problems by using arrays, sometimes nested arrays, to avoid re-computation, and somehow that's supposed to be more "dynamic" than not doing that)