Stops vs thins. An expectorant is a medicine that thins out mucous, making it easier to mobilize and get out. Usually you'll see Guaifenesin as the active ingredient. A cough suppressant stops the body from wanting to cough. This can be ok at night, since you're not supposed to cough anyways, but not a good idea during the day, so mucous keeps moving. Of course, neither is ok for children until at least 4 to 6 y.
Difference... A cough expectorant helps to mobilize the airway mucous so it can be coughed up more easily. A cough suppressant aims to stop the cough. Cough is an important reflex and these medicines should only be taken on the advice of your doctor. Some coughs should not be suppressed and help to cough is usually not necessary.
Expectorants thin. Expectorants make mucus thinner and easier to cough up, and should be used with loose, productive coughs. Suppressants inhibit coughing and are best used with dry, non-productive coughs.