The flu typically presents with a more severe and acute constellation of symptoms then the run-of-the-mill common cold. The flu is caused by the influenza virus, while the common cold is usually caused by a different type of virus such as a rhinovirus or coronavirus (but can rarely be caused by an influenza virus). The flu typically presents with fevers lasting 2-5 days and diffuse muscle aches, and can also cause headaches, gastrointestinal complaints like upset stomach or diarrhea
, joint aches, and coughing. Patients usually remember the exact onset of the illness
(and often describe it like "getting hit by a truck.") This is in contrast to the vast majority of common cold illnesses, which usually cause upper airway congestion, runny nose, and coughing. Fevers are more rare, and if present, are usually low-grade and last less than 48 hours.
Both the common cold and influenza are very contagious and are easily spread between members of the same household. It is good that your children have had the flu vaccine, but you should also take care to reduce the chances of transmission of the virus by following proper hygiene (frequent hand washing with soap and water, coughing into tissues that are quickly throw away, etc).