I was confused about these two radical organizations, so I did some reading on http://en.wikipedia.org
The Taliban was the 1996-2001 governing party of Afghanistan that was unseated in the first gulf war. They persist today as an alternative government (courts, militia) in parts of Afghanistan and are the
identity of the Afgan insurgents.
Al Queda is a stateless radical movement founded in the 1980s by Bin Laden. Al Queda found refuge in Afghanistan under the Taliban when they were kicked out of Sudan in the late 90’s. They now are mostly situated in Afghanistan and Pakistan.
In 1995 Bin Laden/Al Queda took over terrorist operations in Bosnia and began organizing a global jihad. Bin Laden declared Fatwa on America in 1996 and again in 1998. The rest is history.