Yoga and Buddhism are sister traditions which evolved in the same spiritual culture of ancient India. They use many of the same terms and follow many of the same principles and practices. For this reason it is not surprising that many of us born in the West, particularly after an initial exposure, are apt to regard Yoga and Buddhist teachings as almost identical.
We may want to combine their teachings or practices accordingly, as if there were no real differences between them. The differences that have existed between the two systems historically, which have kept them apart as separate traditions, are less obvious to us in the West than are their commonalities. Or those who study one of these traditions may be inclined to see the other as a borrowing from it. Those who study Buddhism may find so much similarity in Yoga that they suspect a strong Buddhist influence on Yoga. Those who study Yoga may find so much similarity in Buddhism that they see a strong yogic influence on Buddhism.
However, the tendency to find commonality between these two great spiritual traditions is not limited to the West. Swami Vivekananda, the first great figure to bring Yoga to the West, examined the Buddhist Mahayana scriptures (Sutras) and found their key teachings and those of Vedanta that he followed to be ultimately in harmony. In recent years with the influx of Tibetan refugees into India, including the Dalai Lama, there has been a new dialogue between the two traditions that is bringing about greater respect between them. Tibetan Buddhists often appear at Hindu religious gatherings and partake in all manner of discussions.