Oblique projections are very different from orthographic projections.

I used to think that orthographic projections mean the image plane is aligned to the axes, and oblique projections have the image plane at some angle to the axes, with isometric projection being a spwcial case of oblique projection where the image plane makes the same angle with all three axes. This is completely wrong!

The following image shows othographic projection in action. The camera rays originating from the image plane are always perpendicular to it. The actual angle of the image plane does not matter.

The following image shows oblique projection. The camera rays may not be perpendicular to the image plane. Orthographic projection is just a special case when the camera rays are perpendicular to the image plane.

The main benefit of oblique projection is that you can draw other faces while preserving the shape of the primary side. Notice that in the hand drawn oblique projection of the cube, the front and the back faces are perfect squares, while in the computer rendered orthographic projection, these faces are rhomboids. To get a perfect representation of the front face in orthographic projection, the side and top faces will have collapse into a line.

References:

• Julien Rippinger's talk on "The Missing Camera or: How I Learned to Stop Worrying and Love Oblique Projection"
• https://en.wikipedia.org/wiki/Oblique_projection