One more time with feeling!
We are coming to the end of my 10-week intro to studio lighting class and I still see confusion between light quality (determined by the size of the light) and contrast (determined by the environment).
Basically, contrast is the depth/darkness/density of the shadows. It is controlled by the environment. If there is a lot of light bouncing around off of the walls, ceiling, floor, or other nearby surfaces the shadows open up. Adding a diffuser to your light spreads the light out to bounce off all those objects to lower the contrast. The bigger and darker the environment you are photographing in, the more contrast you will have. Narrow beam reflectors and grids can be used to control spill (the opposite of adding diffusion) and maintain or increase contrast when working in smaller spaces with light color walls, ceiling, etc. Please, do not add diffusion material in front of your grids!
Quality of light is the transition from highlight to shadow. It is controlled by the size of the light. The larger the light is as seen by the subject, the softer the light is as the light hits the subject from many angles and provides its own fill light. Yes, it lightens the shadows, but the main thing is that it does away with the abrupt edge that you get from a smaller/harder light.
Adding a diffuser such as a scrim or a shower curtain some distance in front of a small light source turns it into a larger source, making the light softer. But diffusion right on the light (which doesn't change the size of the light) will not change the quality of the light. While the shadow is less dark, it still maintains a hard edge if the light source is small.
Some pictures to help explain…