The most important distinction: Watches mean start keeping an eye on the weather and on local weather and news sources. Warnings mean do something NOW.
Watches are for a severe weather threat that is expected in the next few hours. Warnings are for threats that are happening NOW.
Watches are issued for large areas based on a predicted threat. Warnings are issued for much smaller areas based on a specific storm cell's path.
SEVERE THUNDERSTORM lightning, hail, and damaging winds are the biggest threat. Move indoors and stay away from windows. You may also choose to treat it as a tornado warning as the winds can produce tornado like destruction and tornadoes can and do form in areas that are "only" under a severe thunderstorm warning.
TORNADO get to the lowest level possible and put as many walls between you and the outside as possible. If you are in a vehicle, DO NOT take shelter under a highway overpass - wind speeds are dramatically increased underneath.
FLASH FLOOD move to higher ground if you are in a low lying area. DO NOT drive through flooded areas. It takes a disturbingly small amount of water to carry your vehicle away.
TORNADO warnings, SEVERE THUNDERSTORM warnings, and FLASH FLOOD warnings are the warnings that are covered on this page. For all other warnings, visit the warnings map on weather.gov
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