Though there are many different kinds of bicycles, road bikes and mountain bikes are popular for their specialization to their task. As a general rule, those designed for road use will be built to favor speed, while mountain bikes favor stability. These tendencies make sense, considering the purpose of each style of bike. There are four specific areas that will help distinguish the two types.
Shape: Road bikes, having been designed for speed, generally position the rider much closer to the top tube and the pedals. This hunched-over position is more efficient for getting power from the rider's legs, but is also far more taxing on the back than a more upright mountain bike. This design difference is very apparent in the different types of handle bars used for each kind of bike. Those for use on rougher terrain have wide handle bars that allow the rider greater control, as opposed to the bent handle bars of most road models, which are lower and more aerodynamic.
Weight: Where a heavy frame is a huge burden on speed, it is often a necessity for going down the mountain. Bikes designed for this purpose are heavy out of necessity, with wider tires and extensive suspension systems helping to make the ride down the mountain easier to manage. Good bikes for road use will be designed to eliminate as much excess weight as possible, including using materials such as titanium and carbon fiber to allow strength and flexibility in addition to reducing weight.
Tires: The key with mountain bike tires is traction. They're wider and covered with lots of nubby rubber to increase surface area and friction. These qualities will help the rider retain control of the bicycle as he or she careens down the hill. Road bike tires, on the other hand, are generally very thin and very smooth. They rely on the surface of the rubber and the skill of the rider to maintain friction between the bike and the road.
Suspension: Bikes that are truly built for speed will not have any suspension, though they are often built with materials that will absorb vibrations from unevenly paved roads. On the other hand, front shock absorbers, rear suspension, and even unique hybrids will all be available for bikes that are made to tackle the rough mountain surfaces. Suspension is also the area where it's easiest to identify a hybrid or commuter bike. These will have flat handle bars, thin tires, and may or may not include suspension. Some commuter bikes even come with locking suspension, so the rider can choose if they want the extra cushioning of the road.
In the end, a cheaper bike of either type will generally be available for less than $200 US Dollars (USD). On the other hand, very custom or professional-grade models can cost several thousands of dollars. Anyone shopping for a bike should to choose a design based on his or her anticipated needs, and test ride as many different brands and designs as possible. Generally, it's not a bad idea for a rider to buy a bike that he or she can "grow into," in terms of skill or experience. This way, the person can avoid limiting his or her growth as an athlete, or his or her enjoyment of the new bike.