Influenza (flu) and the common cold are both contagious respiratory illnesses, but they are caused by different viruses. Flu is caused by influenza viruses only, whereas the common cold can be caused by a number of different viruses, including rhinoviruses, parainfluenza, and seasonal coronaviruses. Seasonal coronaviruses should not be confused with SARS-COV-2, the virus that causes COVID-19. Because flu and the common cold have similar symptoms, it can be difficult to tell the difference between them based on symptoms alone.
In general, flu is worse than the common cold, and symptoms are typically more intense and begin more abruptly.
Colds are usually milder than flu. People with colds are more likely to have a runny or stuffy nose than people who have the flu.
Read more at: https://www.cdc.gov/flu/symptoms/coldflu.htm