Yes—real blur can absolutely be caused by optics and camera motion, not just by post-processing. But in most cases the blur is not a perfect Gaussian or a true “average blur.”

In photography, real blur is described by the point spread function (PSF), which depends on things like diffraction, lens aberrations, focus error, and motion. That PSF can be quite complex.

Gaussian blur is often used as a mathematical approximation of real optical blur because it is simple and useful in image processing. Some optical effects can resemble a Gaussian distribution—for example certain soft-focus behavior, or special lenses designed to smooth out-of-focus rendering. But Gaussian blur was not created as an exact model of normal lens blur.

Camera jitter can cause blur, but motion blur usually follows the path of the movement rather than forming a pure Gaussian blur.

So the short answer is:

• optical blur is real and happens in-camera
• motion blur is real and happens in-camera
• Gaussian and average blur are commonly used post-processing models
• real-world blur may resemble them, but usually is not exactly the same