Clip space
The coordinate space right after projection, where the GPU clips away whatever falls outside the screen before the perspective divide.
A vertex passes through several coordinate spaces on its way to the screen. Once the vertex shader has applied the projection matrix, the point lands in clip space: four-dimensional (x, y, z, w) and not yet flattened. Clipping is cheap here — anything whose coordinates fall outside the range −w…w is off-screen and discarded, so triangles crossing the edge are sliced cleanly.
Then x, y and z are divided by w (the perspective divide), giving normalised device coordinates and the shrink-with-distance that makes perspective. Clipping before the divide is the whole point: it avoids dividing by zero and handles points behind the camera correctly. It is also where the view frustum is effectively defined.