I beg to disagree.
First, Daniel Pipes, no slacker in this war, usefully points to the distinction. I know of no effective counter argument to his scholarship.
Second, even if you were right, we would want to create an "Allah-Allah-In-Come-Free" zone of purported Islamic moderation. If we back their religion up against a wall, we will have to kill every last one. If we give them a safe zone of non-murderous Islam, it may grow. So even as a strategic deception, the concept of a moderate Islam is useful.
We definitely got us a big, long war ahead of us. We allowed the Germans to remain German after having defeated Nazism. We must allow Muslims to remain Muslims after we have forcibly excised its cancerous types.
The choice of extremist terrorism or moderate civility will need to be put to each Muslim. Let's give them the option of civility.
You just DID agree with me.
We allowed Germany to remain. We did NOT allow Nazism to remain. We tried them at Nuremburg, hanged them, chased them down to the ends of the earth as well as South America. Muslimism is the Nazism of the Arabs. Mohams are the Nazis. We (our fearless forefathers, I mean) didn't allow Nazism to survive and come after us. Why would we allow any other bizarre weird cult that seeks to kill Americans?
With Nazis, we didn't say, ok we know all y'all believe all the Mien Kemph stuff, but we are gonna decide the GOOD Nazis from the BAD nazis---even though they all believe the same stuff. All islams believe the Koran. Yet we are gonna say, there are good Nazis and bad Nazis NOW??
Their founder and their creed say, in clear language, kill Christians, kill Jews, kill Europeans, kill Westerners, kill whitey. Conquer the world and force everyone to convert to towelheadism or else run 'em through with a sword. To believe those who swear by Mohammed and the Koran when they say, oh, we don't REALLY mean it, is to be beguiled much as the masses were by Clinton's "oral sex isn't sex."
It reminds me of the 60's, when militant black muslims would be invited into the homes of liberal pansies like, for example, Leonard Bernstein or Norman Mailer, and the homeys would say, you white m-f, we're gonna kill yo a$$, and the Bernsteins and Jackie Kennedy and the effete upper class would patronizingly say, oh, my you are so right, we deserve it so much, we white people are so bad! Take us now! These people---millions in our own country---PROFESS in WRITING that they will kills us, and we say, "Oh, now, now, dear, dear, you poor people, we know you don't really mean that." No wonder they think Americans are so stupid.
We certainly allow Iraq, Iran, Philippines, Malaysia, Saudia Arabia, Lawrence of Arabia, and the 1001 Arabian Knights all to continue to live in the deserts and bugger their camels and sons, stone their women and go on living in the stone age (while we have to listen libs who tell us constantly how freaking smart these guys are for inventing "zero" and what a great "civilization" they have, whacking the hands off of starving petty thieves.) HOWEVER, if we handle this as you describe---let Germany survive but defeat the Nazis---then, we don't allow their NAZIS, or, in their case, their Mohams, to survive. It is a cult that must be eradicated as we have Nazism and commies.
This is not some isolated incident. They have been coming at us beginning in about the 8th century A.D. To ignore more than 1 millenium of history and assign to it Western views of kindness, goodness, light, and magnanimity, will get us all killed.