There are lots of herbal teas that don't have caffeine already out there. What makes anything "tea" beyond putting some type of [dried, possibly ground-up] plant into a strainer in hot water, then drinking the result?
Just like there are different varieties of grapes more or less adequate to produce some kind of wines, there are different varieties of Camellia Sinensis. All varieties of Camellia Sinensis were thought to contain caffeine, until this specific variety was (re-)discovered.
Herbal teas are basically infusions of any plant that's not Camellia Sinensis.
The word tea has been with us for about 4 centuries now, so it's no wonder it has taken meanings other than its original strict definition. Herbal tea would have been called a potion before the word tea was introduced.
Green, white, black teas are all from the tea plant with different parts of the plant / harvest time / preparation.
Well leaves from a tea bush, obviously.