There are two major types of headset- older, threaded headsets that have a quill that drops into the stem of the fork creating an interference connection, and newer threadless headsets that the stem is bolted and clamped on to. Flat handle bars are preferred by off road cyclists who can ride in a more upright postion whilst still having the controls at their fingertips, whereas drop handlebars offer more cycling positions and are favoured by road cyclists who typically spend more time in the saddle. The controls attached to the different styles of bar are operated and maintained in different ways.
Brakes come in a variety of designs depending on the age and style of your bike. Rim brakes offer more modulation but have less stopping power, so are more suited to riding on the roads. Disc brakes can provide huge amounts of stopping power so are best suited to off road riding, although ‘V’ rim brakes are also well suited to mountain biking. All brakes use a friction system to stop the movement of the wheel, so regular checks of the contact pads should form part of your regular cycle maintenance.