The quick answer is: When there is phlegm or mucus, it is wet. If not, it is dry.
The main difference between a wet (productive) and a dry (non-productive) cough is the presence or lack of mucus. 5
A wet cough is usually seen when cold or flu symptoms are at their worst, which is usually after 4-5 days. During a wet cough, phlegm is produced which is why it is called a “productive” cough. This excess mucus / phlegm needs to be coughed up from the chest and airways. It is most often seen with cold and flu infections and is acute in nature (does not last very long). 5,10,13
A dry cough is when no phlegm is produced (non-productive) from the lungs. It is dry, irritating and can be very tiring. It can be caused by irritations like smoke or dust but is also seen at the beginning or end of a cold or flu. 5,10,13,14,16