Iraqi flags aren't allowed to fly in Iraqi Kurdistan. You can't hear Arabic on the streets or see it written on signs in government buildings. Kurdistan has its own military force (Peshmarga) and schoolchildren start their days by singing a Kurdish national anthem. When Iraqi Kurds say "my country" (which they do often) they mean Kurdistan -- not Iraq.
Is Iraqi Kurdistan actually part of Iraq?
Technically, yes, but it's seriously debatable. Most Iraqi Kurds want to create an independent state from Iraq, even though Saddam's days of oppressing Kurds are over. Iraqi president Jalal Talabani is a Kurd, but does that really matter if only a few Kurds feel any connection to Baghdad or care about what happens there?
Aimee pointed out that the NY Times ran an article indicating Kurdish forces would be sent to Baghdad to help manage the conflict there. Both Talabani and Kurdistan Regional Government president Masood Barzani have rejected sending Kurdish forces outside of Iraqi Kurdistan. There are Kurdish soldiers in the Iraqi army, but according to the leaders Kurdistan's Peshmarga won't go south.
The Kurds don't want to get involved in Iraq's sectarian mess. The prevalent attitude in Iraqi Kurdistan? That's their problem -- not ours.