It is fairly standard to say that the truthmaker of a proposition p is what makes p be true. But suppose we accept a non-deflationary theory of truth on which the claim that p is true is distinct from the claim that p, and is the attribution of the property of truth to p. Now let p be the proposition that there are horses. Then, any horse (or maybe the sum of them all) is a truthmaker for p, or so it is pretty standard to think. But while a horse makes there be horses, a horse is not enough to make it be true that there are horses, since the latter claim involves something other than a horse, namely the proposition p. So, we need to distinguish between making there be horses and making it true that there are horses. A horse suffices for the former task. But for the latter task, we need a horse, p, and whatever relations and properties are involved in the attribution of truth to p (e.g., an instance of a correspondence relation). (I am grateful to Dan Johnson for helping me get clear on what this latter task involves.)
We now have a linguistic question. Is the "truthmaker" of p just a horse, or a horse, p and whatever else is needed? Since "truthmaker" is entirely a stipulative term of art, nothing deeply significant rides on this question, but the question does have two aspects: the sociological question of just how the word "truthmaker" has been used by philosophers, and the question of which way of using the word gets at a more fundamental concept. Say that a "truthmaker(1)" is the concept that goes with the answer "a horse" and a "truthmaker(2)" is the concept that goes with the answer that also includes p. Then there is a natural way of defining truthmakers(2) in terms of truthmakers(1). The truthmaker(2) of p is identical to the truthmaker(1) of the proposition that p is true. One might try to define a truthmaker(1) in terms of taking a truthmaker(2) and subtracting the proposition and the relation, but that definition will be messy and difficult to give. So, it seems that the truthmaker(1) is the more fundamental of the two concepts. Moreover, sociologically, I think "truthmaker(1)" is the right reading of how "truthmaker" has been used, because as a matter of fact most users of truthmakers don't include the proposition and the correspondence relation in the truthmaker.
But now we see that unless we have a deflationary theory of truth, the term "truthmaker", understood as truthmaker(1), is a bit of a misnomer. For the truthmaker of p isn't what makes p be true. It is only a part of what makes p be true: makes p be true is not just the truthmaker(1) but also p and how its related to the truthmaker(1).
It may, of course, turn out that deflationary theories of truth are correct. But unless deflationary theories are established to be true, as much of our theorizing as possible should be compatible with non-deflationary theories as well, and so we should be sensitive to the difference between the condition that p and the condition that p is true.
Two other areas where the distinction could matter are these: (1) Is it a part of our concept of knowledge that if x knows p, then p is true, or should we rather say that if x knows p, then p? (2) Should we require it to be a part of omniscience that for all p, God knows p if p is true, or that for all p, God knows p iff p? With a bivalent logic and an acceptance of Schema (T) as a necessary truth, the answers are going to be necessarily extensionally equivalent. But conceptually there may be a difference, and how we answer (1) and (2) may affect some of our intuitions.
Such sensitivity will also be important when we consider non-bivalent logic, even if we only consider them to dismiss them. For instance, suppose we deny that contingent propositions about the future are true or false, but accept excluded middle. Then if we understand omniscience as implying that God knows p if p is true, God can be omniscient without knowing contingent propositions about the future. But if we understand omniscience as implying that God knows p if p, then omniscience requires God to know some contingent propositions about the future, even if none such are true.