Both; I think.
I can see errors being backspaced out and then being re-typed during live(?) stuff - newcasts and the like.
Pre taped shows have the text generated off line; giving more time to get it right.
My Iphone does pretty well converting what I say into text during messaging.
Imagine what the intelligence of the government has. I bet they have satellites up there specifically set up to pick up all the cell phone conversations, convert them to text and store it in a huge memory bank. When you want to check certain conversations, you have software to search for it, no search warrant needed.