A threaded fork is like what you have there - the top end of the steering tube is threaded, with a large nut and threaded-adjustable bearing cone to set the bearing preload. The typically have a quill-style stem that goeds down through the middle and clamps into the inside of the steer tube. The length of the steer tube is important because too long and the lock nut will bottom out, and too short and it won't reach far enough to thread both the cone and lock nut on. So, they vary in length depending on the length of the bike frame's head tube.
A so called "threadless" headset is what you see on a typical mountain bike and modern road bike. Here, there are no threads on the outside of the steer tube. Instead, these have a star nut down inside the steer tube, which a smaller bolt in the center of the cap threads into. The stem slides around the outside of the steer tube, and bearing preload is set with shims under it. It's all drawn together with the afore mentioned single bolt through the cap. Because the steer tube is unthreaded, it allows manufacturers to use aluminum for it, which wouldn't go over well with a threaded design (which is always steel).
Most bikes have either a 1" (older) or 1-1/8" diameter steer tube. That relates to the diameter of the frame head tube. The head tube itself doesn't really care which style of headset you put in it, as long as the headset is the right diameter and stack height for the length needed.