Wireless and truly wireless: These connect to your devices using Bluetooth, so you’re never physically tethered to your smartphone, tablet, or computer. Wireless headphones don’t use a wire to connect to an audio source, but they do use a wire to connect the two earpieces together. In contrast, “truly” wireless headphones come as two separate earpieces that don’t need wires to connect to anything. Wireless headphones are incredibly affordable; truly wireless headphones can cost anywhere from $100 to $400.
Total harmonic distortion: True, headphones with lower actual total harmonic distortion (THD) will sound better than those with higher THD. But the quoted THD numbers -- "less than 1 percent" -- aren't helpful in predicting sound quality. Listen to recordings of simply recorded acoustic guitar to assess the distortion of one set of headphones versus another. Some will sound appreciably cleaner than others.
If you’ll mostly be using headphones at your desk, install a headphone hook so you can safely stow yours when you’re not using them. Headphones can be fairly fragile, so it’s important to take care of yours and avoid tossing them around. A headphone hook gives your favorite pair a place to hang and creates a fun conversation piece for your workstation.
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.