One type of bicycle is the hybrid. The hybrid typically has smooth, all-terrain tires, flat handlebars and a comfortable seat. It is called a hybrid because it can be ridden on pavement or on some non-paved surfaces.
An urban bicycle is similar to the hybrid but has some type of storage device on the front or back of the bike to carry groceries or other essential items.
The road bike is built for speed on a smooth surface. It has a small seat referred to as a saddle, curved handlebars, and very thin, smooth tires. The higher end road bikes are very lightweight and have better quality components.
A mountain bike is built for off-terrain, trail riding. It has the flat handlebars, fat, knobby tires, and small saddle. Most mountain and road bicyclists prefer to use the clip-less pedals for more efficient peddling.
The tandem bicycle is designed for teamwork. As the name suggests it is designed for two riders on the same bicycle. I have never ridden a tandem bicycle but I somehow think the person on the front does a little more pedaling than the person in the back.