I realize this is an older post, but thought this might be helpful to anyone wondering the same question:
While the previous answers are no doubt valid, there is a more simple reason for the distinction between textarea and input.
As mentioned previously, HTML is used to describe and give as much semantic structure to web content as possible, including input forms. A textarea may be used for input, however a textarea can also be marked as read only via the readonly attribute. The existence of such an attribute would not make any sense for an input type, and thus the distinction.