I wouldn't call myself by either of those titles but I have done a little of both. Some for math modeling and some for computer graphics.
For game programming
1. start by learning your tools.
(Variables, Iteration, Control Flow Statements, Methods, Objects, Pointers, Templates, Data structures)
2. While you do that brush up on your 2d math.
(points, lines, parabola, trigonometry)
3. Start OpenGL learning OpenGL programming (
http://www.lighthouse3d.com/opengl/glut/)
I think its easier than direct X programming
4. Learn about 3-D space and how objects are represented
(
http://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx)
5. Learn Direct X
6. Learn AI
For simulation programming
Do step 1. To me much of simulation doesn't need a GUI. You just have to number crunch)
But if you want a GUI you can use OpenGL.