The way I learned it, if you mix an acid and a base, you get a salt and water. Table salt (NaCl) is the result of mixing hydrochloric acid (HCl) and sodium hydroxide (NaOH):

HCl + NaOH -> HOH (water) + NaCl

But if you mix a different acid and a different base, you'll get a different salt, for example if you mix sulphuric acid and calcium hydroxide, you get calcium sulfate:

H2SO4 + Ca(OH)2 -> 2(HOH) + CaSO4

Calcium sulfate is just a different salt.