Meaning and Truth-Conditionality

One common theory of meaning is this: To know a statement's meaning is to know the conditions under which the statement would be true. So, for example, to know the meaning of the statement "Jones will throw the ball" is to know that such a statement would be true if and only if the event "Jones throwing the ball" obtained. Seems plausible enough.

But there's an obvious difficulty with such a theory. If to know some statement S's meaning one need only know S's necessary and sufficient conditions, how do you explain the fact that the antecedents and consequents of many biconditionals obviously differ in meaning? For example, in the biconditional "I will go to sleep if and only if I take the pills", the statement "I will go to sleep" has "Going to sleep" as its necessary and sufficient conditions, but so does "Taking the pills". So, they both have the same truth-conditions, yet differ in meaning. It's true that they are logically equivalent, but they can't be (by reductio) meaning-equivalent. It follows that truth-conditionality doesn't fully explain the curious explanandum of meaning.

Note: It may be objected that the biconditional "P<->Q" is reducible merely to "(P->Q)&(Q->P)". But this is false. Having the same truth conditions, logically, "P<->Q" is also equivalent to "Q<->P", and (of course) the tautology always holds "P<->P".