The moving coil driver, more commonly referred to as a "dynamic" driver is the most common type used in headphones. It consists of a stationary magnet element affixed to the frame of the headphone, which sets up a static magnetic field. The magnet in headphones is typically composed of ferrite or neodymium. A voice coil, a light coil of wire, is suspended in the magnetic field of the magnet, attached to a diaphragm, typically fabricated from lightweight, high-stiffness-to-mass-ratio cellulose, polymer, carbon material, paper or the like. When the varying current of an audio signal is passed through the coil, it creates a varying magnetic field that reacts against the static magnetic field, exerting a varying force on the coil causing it and the attached diaphragm to vibrate. The vibrating diaphragm pushes on the air to produce sound waves.
Sealed models are ideal for private listening, where you don't want the sound to be heard by other people. Open headphones -- such as foam earpad models and many sports designs -- are acoustically transparent and allow outside sound to be heard by the headphone wearer, and a good deal of the headphones' sound will be audible to anyone near the listener.
The usual way of limiting sound volume on devices driving headphones is by limiting output power. This has the additional undesirable effect of being dependent of the efficiency of the headphones; a device producing the maximum allowed power may not produce adequate volume when paired with low-efficiency, high-impedance equipment, while the same amount of power can reach dangerous levels with very efficient earphones.
Earbuds have small speakers that rest on the ear canal of the wearer. These are usually much less expensive than on-ear and over-ear headphones and reproduce the sound well. However, outside sounds, such as traffic or power tools, can get past the earbuds and interfere with your enjoyment. Earbuds also don't stay in place very well if the wearer is moving much, such as exercising. These also are lower fidelity than on-ear and over-ear headphones.