When chlorine gas (Cl2) or bleach (sodium hypochlorite or NaOCl) is added to water the result is the formation of hypochlorous acid (HClO).
Cl2 + H2O -> HOCl + H+ + Cl-
NaOCl +H2O -> HOCl + Na+ + OH-
Depending on the pH of the solution the hypochlorous acid exists in solution as either hypochlorous acid (HClO) or hypochlorite ion (OCl-).
HOCl < = > OCl- + H+
Free available chlorine refers to the amount of hypochlorous acid AND hypochlorite ions present.
Combined (or bound) available chlorine arises when nitrogen (usually in the form of ammonia) is present to form what are called chloramines (mono-, di-, and trichloramines are possible).
Total available chlorine is the sum of the free available chlorine and the combined available chlorine.