Limes are just lemons picked early.
The lemon's scientific name is Citrus limon. The Key Lime's scientific name is Citrus aurantifolia. While they are both part of the Citrus genus, lemons and limes are different species.
There are two main varieties of Limes, Persian Limes and Mexican Limes.
Mexican Limes are also called "Key Limes." Though Persian Limes look more promising, because they are bigger, their juice is not as flavourful as Mexican Limes.
Limes are picked when they are fully grown, but still green and unripe. If Limes are allowed to fully ripen on the tree, they actually turn from green to yellow. Because of this, some people believe (erroneously) that Limes are just unripe Lemons.
Limes have more sugar and citric acid than lemons.