half equivalence is when we've used (for example) 1/2 equivalent of strong base to titrate a weak acid. thus, we've turned half of our weak acid into its conjugate base and therefore the conjugate base of the weak acid and the weak acid are in equal concentrations. HA = A-
equivalence point is when (for example) we used one equivalent of a strong base to turn all of our weak acid into it's conjugate base. thus, all that is left of my weak acid (HA) is its conjugate base (A-)