LEDs come in two basic categories:
Low power LEDs commonly come in 5 mm size, although they are also available in 3 mm and 8 mm sizes. These are fractional wattage devices, typically 0.1 watt, operate at low current (~20 milliamps) and low voltage (3.2 volts DC), and produce a small amount of light, perhaps 2 to 4 lumens.
High power LEDs come in 1-3 watt packages. They are driven at much higher current, typically 350, 700, or 1000 mA, and—with current technology—can produce 40-80 lumens per 1-watt package.
High power LEDs come in many different shapes and sizes. Some current products from the leading LED manufacturers are shown below.
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Structure of a 5mm type LED.
Source: Lumileds™

Structure of a high-brightness LED.
Source: Lumileds™ |