MIKE MOSS SAYS: Shannon, the differences are related to the expected intensity of the winter weather event and it's impact on travel and safety, and the degree of confidence in the forecast and how soon the event will get underway.
In our area, the National Weather Service will issue a Winter Weather Advisory when any combination of 1 inch or more of snow and/or any accretion of ice in the form of freezing rain and sleet is expected. These conditions are considered to cause inconvenience and require extra caution, but typically aren't life threatening and usually don't impose major disruptions.
Winter Storm Watches and Warnings both have the same criteria, which is an expectation of 4 or more inches of snow and/or one half inch of sleet and/or one quarter inch of freezing rain glaze. These conditions are considered more capable of producing dangerous travel conditions and also, in the case of freezing rain, may lead to power outages. A watch is issued when such conditions are considered possible, usually about 12 to 24 hours before the event gets underway. A warning is issued when the event is considered very likely and is around 6-12 hours from starting or has already gotten underway.
One possible source of confusion on this issue is that the criteria for winter warnings and advisories can vary from one part of the country to another, depending on how well adapted a particular region is for coping with snow and ice. For example, while any snowfall of 4 inches or more would prompt a winter storm warning from the Raleigh NWS, a similar warning from the Buffalo NY NWS office would require an expectation of 7 inches of snow in a 12 hour period or 9 inches in a 24 hour period.
You can see all of the Raleigh NWS advisory/watch/warning criteria at