I seem to recollect as a kid I could adjust the handlebar height because there was an inner bit of telescopic tube that slid out.
That's what's known as a quill stem, which are used with threaded headsets - the stem extended down into the short steerer tube and clamped from the inside using an expander nut/bolt (as opposed to a quill-less stem clamping around the outside of an extended steerer tube, as with a threadless headset).
Basically, with a threaded headset, the forks are held in the frame (and the bearing assemblies held together) by a nut screwing down onto a threaded fork steerer tube, with no steerer protruding above the lock nut. With a threadless headset, the non-threaded steerer protrudes far above the headset and the stem, clamped onto the steerer, keeps the bearing assemblies together (at the right preload) and stops the forks from falling out. Typically, spacers are used below and sometimes above the stem. The top of the spacer/stem stack is just a bit higher than the steerer tube inside them. The steerer tube has a "star-fangled nut" in it (a nut with flanges that grips the inside surface of the steerer tube) and a stem cap is screwed down with a bolt into the star-fangled nut (without the stem being tightened up). This presses the stem cap down onto the stem/spacer stack,gripping the inside of the steerer tube and holding everything together, until the desired bearing preload is attained - then the stem is tightened up to hold everything together for when the bike is in use (the star-fangled nut is pretty much just an aid to holding everything together at the right force until the stem is tightened up to provide a strong and reliable assembly).