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How does a tornado warning differ from a tornado watch?

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Weather forecasting Doppler radars, such as this one operated by the U.S. National Weather Service at New Underwood, South Dakota, extract the Doppler frequency shift of the echo produced by a moving target by noting how much the frequency of the received signal differs from the frequency of the signal that was transmitted.

In the context of weather forecasting, the primary difference between a tornado watch and a tornado warning lies in the immediacy of the threat and the specificity of the forecast.1

Tornado Watch: This is a forecast issued when atmospheric conditions are favorable for the development of tornadoes or severe thunderstorms in a given region. It alerts the public that such weather may occur, but it does not pinpoint specific communities or guarantee that a storm will form. A watch covers a broad area and indicates that warnings may become necessary later.12
Tornado Warning: This is a specific statement that danger is imminent. It is issued when a tornado has been sighted visually or detected by weather radar. A warning is localized to a specific area and calls for immediate action to seek shelter.12

In essence, a watch means "be prepared" because conditions are right for a storm, while a warning means "take action" because a storm is occurring or has been detected.1