The correct word is projection. Here it means the way how to map the 3 dimensional space (the scene, e.g. the world space in front of the camera) into the 2 dimensional space (the screen, e.g. the camera's film).
If the projecting rays are all in parallel, it is called a parallel projection. If the rays pass through a single point, it is called a perspective projection.
If, in a parallel projection, the rays hit the view plane in a 90° angle, it is especially called an orthographic projection. If they instead hit in another angle, it is called an oblique projection.
Hence, "ortho" is (the short name for) a special kind of parallel projections and different from a perspective projection.
How to compute a perspective projection depends on the circumstances. The common thing is that the lateral dimensions are altered with the depth dimension, i.e.
x' = f( x, z ) and y' = f( y, z )
There is no "correct" or "wrong" way per se.
Perspective projection and orthographic projection are both directly supported by graphics APIs; and both are used frequently in games. Pictorial orthographic projections (the axonometric projections from which the (pseudo) isometric and the dimetric projections is often used in 2D games) are possible, too. Oblique projections are also possible, but AFAIK seldom used for games; their original use case is technical drawing.
Not possible are in general all projections that cannot be realized by a homogenous matrix multiplication, like as to my knowledge e.g.
* inverse perspective projection, or
* projections that do not use a flat view plane.
However, also those can simply be used with ray-tracing.
Some literature:
- the internet search engine of your choice
