Here, let me fix that for you.
There, that is more accurate. The Taliban came almost half a decade after the war ended, and fought against the groups that the US backed. The Afghan Civil War was primarily the Taliban, against the forces that wanted a more Westernized nation, primarily led by the Northern Alliance.
You are doing the same mistake that a lot of people make, just classifying all of the Mujahideen as a single group. There were a great many of them, and the US only gave the fundamentalist groups medical supplies and food. The advanced weapons and training went to the more mainstream groups, like those of Ahmad Shah Massoud. Which is why it was a red warning flag to many in the Intelligence community when he was assassinated on 10 September 2001 by Al-Qaeda, at the request of the Taliban. The day before they started a new phase in the Afghan Civil War.
There are times when taking a "Cliff's Notes" approach is a complete and utter failure. You see, most of the fighters there were not "Islamic". They were actually Afghans who supported their King, and wanted to see him restored and a return to Afghanistan being one of the most cosmopolitan countries in the region. The "Islamic" ones saw it as a holy war, and was like a magnet to foreigners who flocked there to fight. The more mainstream groups generally rejected outsiders.