As promised we'll go a bit deeper in the styles of headphones.
Disclaimer: There are some types of HPs to which I'm not particularly fond of, so my experience with them is not as wide as with other styles, but they share certain characteristics that can be easily compared and for this entry I'll stick to 3 of them: comfort, sound & general applications.
Earbuds
This kind of headphone is extremely popular because they are cheap, small, portable, lightweight and if designed and used correctly almost non-intrusive.