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When researching perspective projections on the web, I've come across two different representations. One is unrelated to OpenGL and the other is strictly associated with it.
What is the relation of these two projections? Both are called the same but the matrices are quite different. The first one seems to project unto the xy plane (z=0), the OpenGL one to the z=near plane.
My knowledge in matrices is not that great, but from what I understand the first one refers to Weak-Perspective Projection. This is meant as a "simple" way to give the illusion of 3D. The only thing it does it to make the objects with big Z values appear smaller on the screen, so it divines both the X and Y with Z.
The second matrix is the standard matrix for perspective projection, where it transforms everything in the camera's frustum (depending on its near/far plane, and left/top/right/bottom values) to a cube extending from -1 to 1 in all dimensions. Usually after this transformation, vectors are again (like in Weak-Perspective Projection) divined by Z, but that is not part of this matrix.
The results from the Weak-Perspective Projection are not ideal. Maybe this picture can help understand why:
More information on both matrices on Wikipedia - 3D projection
