We know that world coordinates $(x_w, y_w)$ transform to viewport coordinates $(x_v, y_v)$ which are the physical device coordinates. And during projection, any point $(x, y, z)$ projects to $(x, y)$ onto the projection plane. My question is: Are projection and transformation both the same? Please explain it with a small example. I want to understand intuition rather than details proof.
A projection is a kind of transformation.
A transformation is any modification of a coordinate that expresses that coordinate relative to a coordinate system that is different from its original coordinate system. As such, a transformation involves two coordinate systems: the source and the destination.
A projection is any transformation where the destination coordinate system has fewer dimensions than the source coordinate system. That is, it removes one or more dimensions from the coordinate.