That's a really indirect tie, because the group that became al-Qaeda in Iraq (and later the Islamic State in Iraq, etc.) was an unrelated homegrown Iraqi Islamist group that only adopted the al-Qaeda brand temporarily after al-Qaeda became the dominant public face of anti-American Islamic extremism in the wake of 9/11, dumping that branding as soon as they had their own local success and didn't need the al-Qaeda brand for increased visibility.
Not the same people, obviously. The tie here is the continuation of the same ideology. And while the ideology predates Cold War (Wahhabi, Deobandi, and even Qutb, from whom most of modern extreme Salafi directly derive), its quick proliferation is largely due to outside assistance in proxy wars.
