Talibani are of Afghani origin:
http://www.ccds.charlotte.nc.us/History/MidEast/05/cochran/
True, they later used bases in Pakistan. But they are Afghans.
The Talib is a Pakistani movement. They indoctrinated Afghan refugees into their cause in Pakistani madrassas. True, the Talibs in Afghanistan are mostly Afghans, but they're still the spawn of the Pak Talibs (primarily Jamiat-ul-ulema-e-Islam).
Before the Taliban invasion, Afghanistan was a very moderate Islamic country. The Taliban follow the strictest interpretation of Islam (Deabandi, Wahabbi, Hanbali). Before the Taliban invasion, Afganistan was primarily Hanafi, the most tolerant school of Islam.
http://www.expressnews.ualberta.ca/article.cfm?id=1517
It's not really correct to say the Mujahideen became the Taliban after the ouster of the Soviets. The Mujahideen were a mosaic of warlord armies, not a cohesive organization. The Talibs didn't come on scene until the chaos in the wake of the Soviet withdrawal gave them an opportunity to make their move.
True that the Mujahideen and Talibs for the most part had no animosity toward each other.
Interestingly, Karzai was originally a Talib, but left the movement because he didn't like their harsh way.