Gary Fong Thing-A-Ma-Jig-A-Tron 4000...the cartoon says it all.
There is no small on-flash cap (Sto-Fen, Nikon,Canon) and no small on-Flash Diffuser that can take the place of an umbrella. An umbrella is large, like 30 to 60 inches across the face,and even larger when measured around the curvature ( a pretty common way of specifying umbrella size). A larger light sourfe, in relation to the subject's size, and large in relation to the light-to-subject distance, is what determines how soft a light is.
Take a Fong diffuser. Total area? Maybe 15 square inches. Very small. Beyond 10 feet with a small diffuser like that and you have a small light source that is basically a point light source, and it will cast relatively hard, sharp-edged shadows---once you compensate for the large light loss it causes.
With an umbrella, your light source's size in area is somewhere between 50 and 200 times larger in area, which will keep umbrella lights large and mostly soft across quite long distances. Overcast sunlight shining through low-lying clouds makes for soft lighting much like umbrella lighting; the unobscured sun itself casts shadows much like a small flash with a small diffuser does at 30 feet. Diffusers like Fong or Sto-Fen can create diffused lighting when used at close range,and on very small subjects, but at longer distances and or on larger subjects, their physical size is SO SMALL in relationship TO the subject, that they are, in effect, nothing more than light-sucking, small light sources.
Gary is a good marketer,and always sells a lot of products. But light operates outside his marketing influence. There is no substitute for "size" in light modifiers,and there is no substitute for umbrella or scrim diffusion for people work at distances more than about 10 feet.
