"ISO speed" refers to exposure, not development. A higher-ISO film or sensor setting needs less light to make a usable image, so you can use a shorter exposure time. That’s why it’s called "faster": it allows a faster shutter speed in the same light.

This usage is common in photography. For example, lenses with wider maximum apertures are also called "fast" because they let you make an exposure more quickly.

Historically with film, faster films achieved this with larger light-sensitive silver-halide crystals, which made them more sensitive but also produced more visible grain. Slower films generally gave finer detail but needed more light or longer exposures.

In digital photography, higher ISO settings similarly let you use faster shutter speeds in low light, but the tradeoff is usually more noise and sometimes reduced image quality.

So the word "speed" is about how quickly an exposure can be made under a given lighting condition—not how fast film is processed.