Hi Tad and Nill.
The differences are as follows:
White, is softer and has higher loss of light.
Silver, has more contrast and has less loss of light.
"Black Backed" umbrella, prevents light from spilling/going somewhere you do not want it to and usually will double as a "Shoot-Thru" umbrella.
"Shoot-Thru" umbrella, is softer and has less loss of light than the white.
"Brolly Boxes", are a cross between a "Shoot-Thru" umbrella on the front, a "Black Backed" on the rear, sort of a poor mans soft box.