Here's an easy way to tell the difference, simply by spelling out the word FACTS.
F --- for fever
A --- for severe body aches
C ---- for chills
T --- for tiredness
S --- for a sudden onset of those symptoms.
The most important indicators are fever and sudden onset.
For adults, you most likely won't have a fever with a cold. And a cold typically comes on over a day or so.
The flu comes on very quickly.
Most of the time you WON'T have nausea and vomiting with the flu or a cold, but it can be seen with some flu strains.
No matter what is causing the symptoms, these are signs you want to be seen by a healthcare provider:
*** If you are getting worse after a few days
*** If you have any trouble breathing
*** If you have a cold, but are not improving after a week
That could be a sign it is a bacterial infection and you will need antibiotics.
For kids, err on the side of caution-- any questions, call your pediatrician.