I want to know the difference between k100rs black and white engine ?

Only the color!
The only difference between K100 engines are 8 valves or 16 valves. The 8 valves (early K100rs) has a L-jetronic fuel injection system and the latest 16 valves have a Motronic ignition/injection. Some of the rs engines were painted black (K75s too) and the RT was just aluminum.

I think early RS engines were also just aluminum color. I think the poster is looking for additional clues about that bike he's thinking of buying. That one was a black engine, and had the later seat config, so I thought those two things matched the suspected year of the bike ('86-'88).