Molecules are, indeed, made up of atoms. However, it is not right to say that salt is made up of atoms. Salt gets all of its properties not from the sodium atoms and chlorine atoms that compose the molecule, but from the unique arrangement of sodium and chlorine in a salt MOLECULE. Sodium atoms have NOTHING in common with salt. Chlorine atoms have NOTHING in common with salt. However, when sodium and chlorine atoms come together to make a molecule, then you get salt.

Think about it this way. If I were to take a sample of salt and start splitting it in half, eventually, I would come down to one molecule of salt. At that point, I would still have salt. However, if I were to break that molecule down and make sodium and chlorine, I would NO LONGER have salt. Thus, salt is made of molecules. When you break it down into its constituent atoms, it is no longer salt.