Both are graphics api, meaning that allow you to do 2d/3d graphics.
But there are various differences.
OpenGL has a (imo) more friendly naming convention, being a C style api with all methods starting with glSomething, while DirectX is a lot more ugly and confusing for the neofite.
BUT, with OpenGL you have to deal with driver differences and compatibility issues. You have to "cheat" using stuff like glew to access methods names, hoping that all the stuff you call actually exists at runtime.
DirectX is more reliable: it is installed or not.
BUT OpenGL runs on mac and linux and android and... DirectX is Microsoft only (PC, XBox...)
BUT DirectX manages also sounds and input, while OpenGL doesn't (graphics only).
I think you'd better try the raw basics of both. Put a textured triangle on the screen with both and then choose. You will probably swap between the two many other times.