The Hindu Kush is no part of the Himalayas. Initially it was thought that from Central Asia till east of Bhutan into China it was the same mountain range. This was the result of no real geographical surveys of these vast and very remote regions. Later, owing to proper geographical surveys, it was realised that by every definition of a mountain range this whole stretch consisted of many separate and different mountain ranges, e.g. The Pamir range in Central Asia and northern Afghanistan, The Alai north of the Pamir, The Tein-Shan north of The Alai, The Hindu Kush along the border between Pakistan and Afghanistan, The Karakoram along the border of Pakistan and China and then onto IOK, The Kunlun Shan running north of the Karakoram in China and then the Himalayas starting in Pakistan and then running through IOK, onto the Chinese borders with India, Nepal, India again, Bhutan and then ending in China (There are then sub-ranges within these distinct ranges, e.g. the Muztagh Range in the Karakoram). Some of these ranges are still confused as parts of the others (e.g. The Kunlun Shan a part of The Karakoram), however it is unanimously accepted by all authorities that The Pamir, The Hindu Kush, The Karakoram and the Himalayas are four completely separate and distinct ranges and not a part of any of the others.
The layman of the world, however, has been slow to understand these revelations since not a lot of people actually understand how mountain ranges work and also because man is slow to learn anything. The non-scientific terms 'The Greater Himalayan Region' and 'The Greater Himalayan Mountain System' still in use to clump all these ranges together for the sake of convenience have also not helped the matter.
A completely defunct classification of the ranges, not accepted anymore.