There is now such a thing as American Buddhism but it is more commonly referred to as Western Buddhism since it includes all Western country practices as taught by the Venerable Chogyam Trungpa Rinpoche who was the first Tibetan to come to the West and teach Buddhism.
Buddhism as Lifestyle
It is important to understand that Buddhism is more a system of beliefs than it is a religion. It is a way that you can think and live in order to attain a particular goal. Now, the goal is what seems more like a religion and more than just a lifestyle and maybe it is.
The goal is to attain liberation from samsara which is the endless cycle of suffering in birth and death. According to Buddhist belief, people continue to return and be reborn as a matter of what karma dictates.
Karma is basically action and it is the actions of ones lives that determine what realms one will be reborn in. The human realm is just one of these realms.
Buddhism in the East
The Tibetan tradition of Buddhism is perhaps the most colorful and interesting as well as mystical of all the types of Buddhism known. It is still enshrouded in mystery for many except those who have been initiated into the Secret Mantra by the highest Tibetan Lamas.
One of these Tibetans, Chogyam Trungpa Rinpoche (Rinpoche means “precious one” or “precious teacher”) came to Scotland in 1967 and founded the very first Tibetan Buddhist school in the West.
As it turned out, the Buddhism of the East was not easily understood by Westerners and so Chogyam Trungpa Rinpoche translated it for Western view. Later, he brought it to America and fleshed it out from the Eastern traditional methods.
Buddhism in the West
Unlike in the East, Westerners were not able to live in monasteries and nunneries for their entire lives. The dominating religions of the West were and still are Judeo-Christian religions so there was little to no way for Westerners to understand the practices.
It was thanks to the Venerable Chogyam Trungpa Rinpoche who studied English studies at Oxford University in England that the teachings were translated. He soon gained a strong following in the West and, by the mid 1970’s he had formed the school of Shambhala Buddhism in the west.
This is what is now known as “Western Buddhism” and is sometimes mistakenly called “American Buddhism.” It is actually Buddhism for the west and it is missing much of the colorful traditions and symbolism of traditional Tibetan Buddhist practices.
Demystification for the Rest of Us
Since the Eastern form of thought is not the same as the Western form of thought and Westerners are not able to practice Buddhism in monastic settings, there was a need to strip the Tibetan practices bare of all the ritual and symbolism right down to only the essentials. That meant a totally new type of Buddhism was needed.
It was taught by Chogyam Trungpa Rinpoche and the teachings still grow to this day.