Chemical symbol represents an element while formula represents a compound.
For eg. - Chemical symbol for oxygen is O, but when we talk about water which is a compound , we say, chemical formula of water is H2O.
Chemical symbols-
Hydrogen -H
Sodium- Na
Calcium - Ca
Potassium - K
Nitrogen - N
And Some of Chemical formula for the compound
Sodium chloride - NaCl
Ammonia - NH3
Calcium oxide - CaO