Marketed claims such as 'frequency response 4 Hz to 20 kHz' are usually overstatements; the product's response at frequencies lower than 20 Hz is typically very small. Headphones are also useful for video games that use 3D positional audio processing algorithms, as they allow players to better judge the position of an off-screen sound source (such as the footsteps of an opponent or their gunfire).
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.