According to John M. Frame, one of the leading Calvinist theologians (who also has a M.Phil from Yale), apologetics of any type focuses primarily on one of three approaches: proof, defense, and offense, though any complete apologetics will include all three. In the first, the defender of faith attempts to offer proof in support of her position which might persuade the interlocutor to concede a key point or accept a theory on faith altogether. In the second, the defender of faith seeks merely to provide a reasoned account for why she is justified, through reason or faith, in holding a given position or belief. Finally, a defender of faith assuming an offensive approach attempts to actively discredit contrary evidence in order to strengthen the case for the given claim.
Regardless of the approach, it is important to note that Frame views the purpose of apologetics as twofold; to at once offer a public recognition of Christ as the son of God and the Christian faith, as well as to offer “a reason for [Christian] hope.” Frame champions ‘Presuppositional Apologetics.’ This form of apologetics has gained more notoriety after the debates between Douglas Wilson and the late Christopher Hitchens were published and also featured in the film Collision: Hitchens vs. Wilson. Though he won’t own up to it, William Lane Craig’s defenses of Christianity often retreat to such a position and he is widely considered one of the foremost Christian Apologists currently on the scene.
I certainly cannot answer for Aaron, but in my opinion the difference between an Apologist and a Philosopher of Religion is that while the latter might argue in favor of belief itself, or particular types of belief as holding varying divisions of epistemic weight, the former argues from a position of already having accepted the truth of some religious claim and seeks only to defend that specific claim. Any personal religious affiliation on the part of the Philosopher ought to be ancillary to whatever claim is being made. A Christian Apologist is first and foremost interested in defending Christianity and in some cases employs circular argumentation (i.e. Frame, Wilson, and other presuppositionalists) whereas a Philosopher ought to pursue sound argumentation and discard those beliefs which fail to be upheld by reason and analysis.
Not all Apologists offer irrational arguments. However, when one claims some premise to be irrefutably true based on subjective/intrapersonal experience or an appeal to the authority of some bit of text, how well-reasoned can such an argument be?
Essentially, I agree with Jared here. The difference between an apologist and a philosopher is that the former begins with the truth and proceeds to defend it at all costs. The latter knows that doubt is an art that has to be acquired with difficulty and that truth (if there is such a thing) is a difficult thing to obtain. The business of philosophy is really about developing systematic techniques through which to assess arguments and evidence. The business of apology is the development of ways to avoid critically assessing one’s beliefs.
Plantinga’s epistemology (and, I would argue, all reformed epistemology) is base apology for Christian theism. On the other hand, Swinburne approaches the theism as a philosopher who happens to find the arguments and evidence in favor of Christian theism persuasive.