As I understand it:
Tea leaves naturally contain caffeine. However, the less the leaves are oxidized, the less caffeine they generally have.
Black teas are the most oxidized, and therefore have the most caffeine.
Oolong teas are only somewhat oxidized, and therefore have less caffeine than green tea, but do still contain some caffeine.
Green teas are not oxidized at all, and therefore have a "baseline" caffeine content.
White teas are also not oxidized at all, but are created from younger leaves, and therefore contain less caffeine than green tea.
Decaf tea, no matter what variety, still contains a small amount of caffeine.
Teas such as rooibos, honeybush, and herbals are not really tea at all and don't contain any caffeine.
Hope this helps.