To illustrate the difference, consider the following imaginary (yet altogether typical) dialogues.
CHRISTIAN: The Qur'an says, "Fight those who do not believe" (9:29). This means that Muslims are supposed to fight unbelievers.
MUSLIM: No, it simply meant that one particular group of Muslims was supposed to fight a particular group of Christians that was attacking them at a particular time.
CHRISTIAN: That's not what it says at all.
MUSLIM: But that's what it means.
CHRISTIAN: Can you give me a Muslim source saying that?
MUSLIM: No, but that's what it means.
CHRISTIAN: Well, since you can't give any Muslim sources that agree with your interpretation, let me give you some commentaries that agree with my interpretation. Ibn Kathir says . . .
MUSLIM: Ibn Kathir! Who cares what Ibn Kathir or any other Muslim commentator says!
CHRISTIAN: It seems you don't want to listen to classical Muslim commentators because they say that "Fight those who do not believe" means "Fight those who do not believe."
MUSLIM: Enough of this paranoid, Islamophobic racism!
MUSLIM: Christianity is a religion of violence and bloodshed!
CHRISTIAN: Nonsense. Jesus said that we are to love our enemies and to pray for those who persecute us (Matthew 5:43-48). He said that His followers do not fight, because the Kingdom of God is not an earthly kingdom (John 18:36). When one of His followers used the sword, Jesus condemned the attack (Matthew 26:52). Paul said that we "do not war according to the flesh (2 Corinthians 10:3-4).
MUSLIM: Yes, but all of those verses mean the opposite of what they actually say. They really mean that Christians are to hate their enemies and that they are to spread Christianity through the sword.
CHRISTIAN: That's not what the verses say.
MUSLIM: But that's what they mean. And to show you that Christians are supposed to hate their enemies and spread Christianity through the sword, let me quote a Christian theologian from a thousand years after the New Testament was written.
Do you see the difference? When Christians appeal to Muslim commentators, it's to show that verses of the Qur'an mean what they say, and that Muslim attempts to reinterpret embarrassing verses are a modern phenomenon, often influenced by Western values. When Muslims appeal to Christian commentators, it's to show that verses of the Bible can't mean what they say, and that Christian attempts to follow what the Bible actually says are misguided.
Consider a few more illustrations.
(1) The Qur'an commands Muslims to beat rebellious wives (4:34). Westernized Muslims today say that this verse simply refers to a light, symbolic tapping with a toothbrush. Here Christians go to Muslim commentaries showing that the verse means exactly what it says, and Muslims reject the commentaries, choosing instead to go against the obvious meaning of the Qur'an.
(2) The Qur'an says that there is "no compulsion in religion" (2:256). Since the Qur'an plainly declares that earlier verses are abrogated by conflicting later verses, it's obvious that 2:256 was abrogated by verses such as 9:5, 9:29, 9:73, and 9:123. But Muslims don't want to admit that the few peaceful teachings of the Qur'an have been abrogated, so they reinterpret abrogation, saying that it only applies to the Qur'an abrogating previous scriptures. Thus the Christian pulls out Tafsir Ibn Abbas, Tafsir Jalalayn, and Tafsir Ibn Kathir to show that abrogation applies to earlier verses of the Qur'an, and commentaries are produced to show that 2:256 has either been abrogated or that it only applies to "People of the Book" who are paying the Jizyah. At this point, Muslims reject all of their greatest commentators, ignore the Qur'anic context, pound their fists on the table, declare that 2:256 is valid towards all people, use 2:256 to reinterpret clear Qur'anic commands to violence, and finally declare that Islam is a religion of peace and that anyone who disagrees is an Islamophobe!
(3) According to the Qur'an, men can have sex with prepubescent girls (65:4). Though the verse clearly discusses girls who haven't yet reached the age of puberty, Westernized Muslim proclaim that it doesn't mean this at all. Here we consult Tafsir Ibn Kathir, Tafsir Ibn Abbas, and Tafsir Jalalayn, and we find that all of them understood 65:4 to refer to sex with prepubescent girls (i.e. exactly what the verse says). Modern Muslims, however, don't want to accept this, and so they once again throw out their greatest commentators.
(4) The Bible commands husbands to love our wives as Christ loved the church (Ephesians 5:25), to be ready to lay down our lives for them, and not to be harsh with them (Colossians 3:19). The Bible declares that both men and women are created in the image of God (Genesis 1:27), and that in Christ there is neither male nor female (Galatians 3:28). To show that these verses can't possibly mean what they say and that the Bible condemns women as the inferior sexual slaves of abusive men, Muslims go on to quote later Christian commentators who ignore the clear teachings of the Bible.
To sum up, Christians want to accurately report the meaning of both the Bible and the Qur'an, in order to allow people to make an informed choice between the two religions. Hence, Christians attempt to read both Christian and Muslim sources in context and to provide a clear account of what the religions teach. Muslims want to misrepresent both the Bible and the Qur'an in order to keep people from honestly assessing the evidence. Thus, Muslims distort the teachings of the Bible by appealing to extra-Biblical sources, and they reject extra-Qur'anic sources which declare that the Qur'an means what it says.
It could be useful to come up with some sort of rule about how to use sources outside of the Bible and the Qur'an. It might run as follows:
"Scripture is to be interpreted primarily by other scripture. That is, a verse is to be evaluated according to its context in the passage and in light of other verses in the text. If a verse is ambiguous, it should be interpreted based on clear verses addressing the same topic. Commentaries may be consulted here to provide the historical context, which reflects what the verse would have meant to the people to whom it was addressed. When someone attempts to deviate from the clear contextual meaning of a verse, commentaries should be provided to show that orthodox scholars prior to modern influence agreed with the clear contextual meaning, and that modern reinterpretations are therefore probably wrong. When a commentary presents an interpretation that conflicts with the clear contextual meaning, the commentary is to be rejected."
For some excellent examples of how these conflicting uses of extra-Biblical and extra-Qur'anic sources play out in debate, please watch our debate with Abdullah and Yahya on whether Islam is a religion of peace, as well as my debate with Abdullah on whether Christianity is a religion of peace. Pay attention to how sources are used. I haven't seen Mary Jo's debate with Tabasum yet, but I suspect that the same would apply to that debate. That is, I suspect that Mary Jo uses extra-Qur'anic sources to show that the Qur'an means what it says, and that Tabasum uses extra-Biblical sources in order to distort what Christianity actually teaches. Of course, this is simply a prediction based on my working hypothesis (which, in turn, is based on past observations). Anyone know whether my prediction is confirmed?