Ditto everything Scruff said, and here's my two cents to boot:
The extent of processing undergone by black teas is (usually) much higher than anything oolongs, greens, and whites go through. Consequently, black tea leaves are a bit more 'broken up' on the cellular level, which allows those cell contents to infuse into water more readily. I'd bet my car that this accounts for the higher amount of caffeine in black teas, followed by (you guessed it), oolong, green, then white.
Amounts of caffeine can also differ across the many varietals of the tea plant itself, but I would still put my money on the advanced cell rupture of blacks to account for the caffeine in the cup.