There are many types of BMX Stems. After over 30 years of selling and repairing bikes here is a brief summery.
Threadless stems are most common on bikes built now and up to about 20 years ago. These stems replaced the shafted type of stem. Threadless means the fork they attach to has no threads on it. Threadless stems clamp to the fork with side bolts and a pressure cap on top of the stem. Threadless stems use a threadless headset to build the front end of the bicycle. The top cap is tightened or loosened to adjust the headset bearings so the fork operates smoothly with no play or rock. This new category is by far the best in stems of strength, light weight and assembly.
The shafted type of stem was used in the 1970s to about the year 2000. This type of stem has a 4inch shaft that slides into the steerer tube of the fork. It is tightened with a long bolt that has an expander wedge at the bottom. The stem tightens as you tighten the wedge bolt tight. These stems were also called goose necks by many bicycle enthusiasts.
These stems use a threaded type headset. A threaded headset is independent of the stem. It only connects the frame to the work and then you install the stem. The threadless stem is what secures the headset to the fork on the modern threadless stem. The Goose Neck is used on all the old school retro BMX, Mountain and Road Bike builds.
The above stems are made in many different lengths, sizes and colors. The length you choose depends on the reach you want on your handlebars. The sizes depend on your handlebar clamping diameter and the steerer tube size. The most common steerer tube size on adult bikes is 1 1/8″ threadless. The most common bar clamp size is 22.2mm but many bikes are wider especially mountain and downhill bikes. The strongest handlebars are chromoly steel and the lightest are carbon fiber.