What is the differences between science computer and mathematics computational programmes?

Computer science (CS) has many areas, including theoretical CS (TCS) that includes algorithm design and analysis. It also include systems CS, such as operating systems, computer architecture (overlapping with computer engineering), embedded systems, computer networks, and compiler design. It also has areas that can be classified into both of these areas, such as Artificial Intelligence and Formal Verification.

On the other hand, mathematic computational is about mathematical and computer modeling, and developing software to analyze these models. Basically, simulate the computer models (you will have to develop the simulator, or use a simulator) or analyze the mathematical formulation associated with these models by solving it as a math problem via computer programming. You do not have to design new algorithms, if algorithms exist for analyzing your mathematical and computer models unless you want the analysis to be done better and/or faster.