Differently prepared tea leaves from the plant Camellia sinensis produce their own kinds of tea. Most of the specific types of tea are distinguished by alternate preparations of the tea leaf. One type of tea is from the tea buds, and another is actually from another plant.
Most teas have caffeine from the oxidation that occurs in processing. In moderation, caffeine can be a benefit, but the large number of caffeinated drinks consumed daily by the average person produces caffeine overload and the detrimental side effects. How you brew your tea also alters the amount of caffeine per cup, and a complementary chemical in tea provides an overall stimulant rather than the brain-and-muscle focus of strict caffeine.
Warning: the chemicals used to decaffeinate drinks cannot remove all caffeine from the beverage, and the chemicals themselves are suspected to have worse effects on the body than the original caffeine and are known to destroy most of the health benefits.
To naturally lower the caffeine content of your tea, pour boiling water over your tea, let it steep for 45 seconds, then pour off the water and brew your tea for drinking. You will sacrifice some of the flavor for this, though; the lower the quality of the tea, the more flavor you will lose.
Teas made from things other than tea leaves are universally called "herbal teas" or "infusion teas" despite arguments that they actually are not tea. The term "true tea" explicitly excludes herbal tea. The caffeine-free teas are actually herbal teas.
The types of teas are black, chai, green, oolong, red (rooibos), tazo, and white.
However, even red (rooibos) tea can be argued to not be tea by some who argue that "true teas" only refer to those teas that are made from the Chinese and Indian versions of the single species of the tea plant Camellia sinensis or hybrids of the two.