The two ions to be distinguished are : Chloride ion and sulphate ion
The chloride ion can be identified by addition of silver nitrate to the solution containing chloride ion
On addition of silver nitrate, chloride ion will react with silver ions to form a white precipitate of silver chloride
The reaction is
Ag+ (a) + Cl-(aq) ---> AgCl(s)
the solution containing sulphate ion can be identified by adding barium chloride
Ba+2 + SO4^-2 ----> BaSO4(s), white ppt
thus barium chloride reacts with sulphate ion to form white ppt