The DNC recently took the extraordinary step of making
an ad that included a clip of President Bush saying "We do not fight against Islam." In the video, the Democratic Party was using Bush to convey the idea that he was more in line with their own denials about Islamic terrorism than today's Republicans are.
But, unlike today's Democrats, Bush never denied the existence of
any connection between Islam and the terrorists. By distinguishing between radical (or "extremist") Islam and Islam, Bush made a distinction that was politically correct at the time and for years to come---until the Obama administration decided that Bush's formulation was unacceptable, and it was forbidden to draw the obvious connection between Islam and terrorists who said they were acting in the name of Islam.
In the immediate post-9/11 weeks and months, Bush faced a very different situation than today: he was dealing with a country and a Congress playing catch-up in learning about the menace of Islamist terrorism and what it really was capable of, a need to rally together all Americans in the wake of a terrorist attack that has still never been surpassed in magnitude and daring, the very real fear of a major backlash against innocent Muslims in the US, and the goal of gaining worldwide allies (including many Muslim countries) in fighting the country that had harbored Bin Laden---Afghanistan---as well as fighting Islamic terrorists as a whole.