Two words, very different actions. Get this distinction right and it can save your life.
Conditions are favorable for tornadoes to develop in your area.
A tornado has been sighted or indicated by radar. Take shelter NOW.
Watch = "watch out." Conditions are RIGHT for a tornado. Stay alert.
Warning = "warned you." A tornado is HAPPENING. Take shelter.
Watches are issued for large areas (multiple counties or a whole state) hours ahead by the Storm Prediction Center. Warnings are issued for small, specific polygons (a few square miles) by the local NWS office, usually with minutes of lead time.
Same logic applies to severe thunderstorms:
Since a tornado watch is issued when conditions are also right for tornadoes, a Tornado Watch implies a Severe Thunderstorm Watch too. But you can have a Severe Thunderstorm Watch without a Tornado Watch.
When the atmosphere is exceptionally dangerous — the kind of setup that produces long-track EF3+ tornadoes — the SPC issues a Particularly Dangerous Situation (PDS) Watch. It's a rare and serious escalation of a Tornado Watch, and it means to treat the day like a day with active warnings. April 27, 2011 was a PDS day.
When a large, violent, damaging tornado is confirmed on the ground and headed toward a populated area, the NWS may issue a Tornado Emergency — a rare enhanced Tornado Warning. It usually contains phrases like "MASS CASUALTIES ARE POSSIBLE" and means the situation is life-threatening for anyone in the path. Take shelter with the best protection available.