A headphone with an In-Line Microphone and Controls will always be a preferred option as its built to control a portable music player and take calls on a smartphone enabling you to be completely hands-free. Usually the controls are on the front and mic on the backside of the remote. It is strategically placed on the right side, in close enough proximity to pick up the voice input.
If you have a headphone and would like to make it a headset, there are various mic adaptors available to enable a mic function.
While choosing a microphone, be sure that your device is supported by the headphones you buy. Some headphones will only support iPhones, which means that the volume and other remote controls won't work if you plug them into your Android or Nokia smartphones.
Headphones with a one-button mic will have limited controls as compared to a 3 button one. The one button will usually let you answer/drop calls, play/pause your music and some may let you change tracks. A three button remote will let you increase volumes and allow more functions which differ from brand to brand.
PC Headsets come with a noise cancelling boom microphone for clear speech during Skype calls. These mics stick out of the headphone and aren't in-line like mobile headsets. The controls may be limited to just a mute button and maybe volume controls.