We'll just talk about the main three types of bikes and their specificities; city, road and mountain bikes. You have subcategories and hybrids of these and other specific bikes like BMX, pista, cargos or tandems.
They are robust bikes, with a good handling and pretty stable. Their bigger tyres and large saddles make the rides comfy. The sitted position makes you aware of what's happening around you, therefore they are great bikes for commuting and strolling.
The bar between the saddle and the handlebar can be low on women bikes and high on men bikes.
Road bikes are light and reactive. The thin tyres make them a perfect fit for clean and smooth roads. The laying down position gives you more power, they are dynamite on open roads and to ride long distances.
A popular subcategory of road bikes is the fixie that in it's more simple form has one chainring, one cog (we'll have a terminology chapter later on), no freewheel and no brakes.
They are bulky and solid bikes. The thick and grooved tyres allow you to get off the road. The semi-sitted position gives you a good compromise between power and control. They are fantastic bikes for nature rides.
These bikes are oftenly suspended, front and/or center, to smoothen the ride on rugged terrain.