Yes, the Taliban are present on both sides, but the strange distinction of "Good Taliban and Bad Taliban" exists only in Pakistan. This distinction is not only propagated by some destructive personalities in the media but is also part of the official policy of Pakistan. Sadly, a great number of people fall for it hook, line, and sinker, and no amount of tragedy seems enough to change their minds.
Very recently the Foreign Minister of Pakistan went on record to say that in the operation Zarb-e-Azb they will not be targeting the Good Taliban. What is surprising is that they expect the outcome of this view to be different from what has been going on in Pakistan for over a decade.