Perspective projection deals with the depth of the image. Artists use perspective projection to draw or analyse 3D scenes. Though this projection creates realistic views, it fails to preserve the proportions of the object dimensions. In the demo given below, increase the distance from the camera slider and compare yourself the difference in the image as the distance is increased. Similarly change the slider values and you will understand how the perspective projection displays 3D images well but at the same time, the proportion of the object dimensions vary.
Orthographic projection is a type of parallel projection. Orthographic projections are most often used to produce the front, side and top views of an object. The front, side and rear projections are called elevations. The top is called plan. Orthographic projections that display more than one face of the object are called axonometric projections. The most commonly used axonometric projection is isometric projection. Here, as we move the sliders and observe the changes in the scene, the object does not change its dimensions even after rotating the cube. Thus, it is mostly used by architects for the better measure of the plan drawn.
The concept behind the working of VR headset is that stereoscopic projection is displayed which splits VR screen into two, with an individual view for each eye to create a 3D perspective. This is done using the angle and type of lenses in the headset. The lenses distortthe two independent images, one for each side, into the correct shape for how our eyes would otherwise see the real world. The actual images for each eye are displayed slightly off from one another. If you close one eye back and forth in the headset, you can see the objects in VR dance back and forth. It's this principle that lets the VR be 3D.