Main types of bicycles are road, mountain, commuter/comfort and fitness bikes. There are more specific types and other names for bike types within that, such as urban bikes (same as commuter bikes), cruiser bikes, dual-sport bikes, hybrid bikes, fixed-gear bikes, cyclo-cross bikes, adventure road bikes (aka all-road bikes, gravel bikes), road bikes, touring bikes and specialty bikes, like BMX.
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.