According to this picture it is the "stud", but others call it the "ball stud" due to the ball machined on the bottom end, where the tie rod end is formed around the ball portion.
tie-rod2-357x372.jpg

Yes, all tie rod ball studs are tapered; and No, not all tie rod ends have the same thread size on either the ball stud, or on the female thread for the tie rod connection. The sizes of these threaded connectors will be larger depending on the load being carried, i.e. you'll have a larger castle nut on a 1T truck than you'll find on your average sedan, and the one on your econobox may be even smaller, depending on the weight and load rating of the front end compenents.