"The designation “Buddhism” originates in the West, not the East. In short, it is a construct of the minds of scholars in the West. There is no definitive evidence, for instance, that Tibetans, Indians, Sinhalese, or Chinese referred to or conceived of themselves as Buddhists before they were given this label by Westerners."What is the difference between Eastern Buddhism (India/China/Japanese/Thai/etc) if I got my geo' correct, and Western (Some parts of Europe/American/etc) Buddhism?
Olson, C. (2005). The Different Paths of Buddhism: A Narrative-Historical Introduction. Rutgers University Press.
"What many Americans and Europeans often understand by the term “Buddhism,” however, is actually a modern hybrid tradition with roots in the European Enlightenment no less than the Buddha’s enlightenment, in Romanticism and transcendentalism as much as the Pali canon, and in the clash of Asian cultures and colonial powers as much as in mindfulness and meditation."
McMahan, D. L. (2008). The Making of Buddhist Modernism. Oxford University Press.
"the term ‘Buddhism’ seems to have arisen at around the same time as its sibling ‘Hinduism’, and it is by no means a straightforward task to find a meaningful version of the term (or indeed for the terms ‘religion’ or ‘mysticism’) in Asian languages. This is not, as has often been stated, merely a problem of translation but one of social identity. It is not clear that the Tibetans, the Sinhalese or the Chinese conceived of themselves as ‘Buddhists’ before they were so labelled by Westerners."
King, R. (1999). Orientalism and Religion: Postcolonial Theory, India and "The Mystic East". Routledge.