Different Uzbeks. The Northen Alliance Uzbeks were Afghanis of Uzbek ethnicity. They were led by Rashid Dostum, an Afghani uzbek politician.
The Uzbek militants in Pakistan are not affiliated with Dostum - they are actual Uzbekistanis from Uzbekistan, not Afghanistan. They were forced out of their country by its dictator after the militant effort to overthrow the Uzbek government failed, and they found welcome and shelter initially from Al-Qaeda in the late 90s and following the rapid demise of Al-Qaeda earlier this decade, in the communities that were sympathetic to Al-Qaeda.
These are Uzbeks in exile - they can't return to Uzbekistan because the government wants to kill them, but having failed to create an "Islamic" state by force in Uzbekistan they are trying to help the Pakistani Taliban do the same in the FATA.
They should all be killed off anyways. They have had complicity in the slaughter of Shi'a as well.
The more they are killed off, the better the world will be.