There are two common types of cough, a dry, tickly cough and a chesty, mucus cough, and they’re pretty easy to tell apart.
If you have a dry cough you won’t produce any mucus or phlegm when you cough.
On the other hand, if you have a chesty cough you’ll bring up phlegm when you have a good coughing session.
Different types of cough need different types of cough medicine, which is why there are so many available.