There are two teleological concepts: that of a telos and that of proper function. Each of them helps us make certain teleological judgments. Do we need them both? Could we, for instance, define the telos of a system as what is achieved when the system is properly functioning? Or define proper function as the achievement of the telos in a system and all its (relevant?) subsystems?
I don't know for sure that we need them both, but neither of the two specific proposals is correct. Consider the case of an excellent mathematician is striving to solve an extremely difficult mathematical problem, her mathematical faculties are all working properly, but she fails. It is not a necessary condition for the proper function of mathematical faculties that they be able to solve every mathematical problem there is. Both of the attempted reductions neglect the phenomenon that our teleologies can push us above our proper functioning. An excellent mathematician or athlete may already be functioning above our proper level of functioning, but nonetheless there will be telê that she doesn't have fulfilled. (Though, perhaps, we may want to say that all humans are mathematically and athletically defective, due to the Fall, in which case we could maintain that the mathematician is not functioning properly if there are any soluble problems she can't solve. But even if this view of humans is true, we could imagine that mathematicians of some other species are functioning properly and yet failing to solve problems.)
It seems that we need the concept of proper function to tell us what is good enough, what is normal. But we need the concept of a telos to supply us with comparisons between instances of proper function. The mathematician who solves and who fails to solve are both functioning properly, are both functioning sufficiently well, but the one who solves is functioning better--precisely because she achieves her telos in respect of that process. Or, alternately, we may say that both are functioning properly, but one is functioning merely normally and the other supernormally--again, a distinction that mere proper function does not seem capable of making.
Maybe there is a more clever way of relating the two concepts.