A Severe Thunderstorm Watch is issued when severe thunderstorms are possible in and near the watch area. It does not mean that they will occur - It only means they are possible.
A Severe Thunderstorm Warning is issued when severe thunderstorms are occurring or imminent in the warning area.
Severe thunderstorms are defined as follows:
1) Winds of 58 mph or higher
AND/OR
2) Hail 1 inch in diameter (size of a quarter) or larger.
Although all severe thunderstorms can produce tornadoes, sometimes there's an increased risk for these storms to rotate - this sets the stage for tornado watches.
A Tornado Watch is issued when severe thunderstorms and tornadoes are possible in and near the watch area. It does not mean that they will occur - it only means they are possible.
A Tornado Warning is issued when a tornado is imminent. When a tornado warning is issued, seek safe shelter immediately.