I heard the term "dynamic programming" and naively assumed it had to do with programming in the sense of computer programming (as that's the only way I've heard the word used before. Used to work with software engineers a lot). I was told (after being laughed at a bit) that when a math/econ person says "dynamic programming" it has nothing to do with computer programming, and it is just a technique for solving complicated problems in a dynamic setting. However, I have read the wikipedia page and I don't understand the difference. Isn't the computational approach the same at the mathematical one, just wisely using the computer as an assist to execute the algorithm?
If it's not too much to ask, what exactly do the terms "programming" and "control" mean in this area?