Vietnam is alone in Southeast Asia in that its language is predominantly a Chinese language (having switched over to a heavily altered version of the Roman alphabet after French colonization) and Vietnamese society and traditions largely stem from the Chinese cultural sphere. For example, like China, Korea, and Japan, Vietnam had a Confucian bureaucratic examination system to find public servants. Ho Chi Minh's father was one of them.

In the rest of southeast Asia - Laos, Cambodia, Thailand, Burma, though also Sri Lanka, Malaysia, and Indonesia to varying degrees can fit in here - is dominated more by Indian cultural influence, probably an accident of geography. The geography in general makes it difficult to say anything cohesive about this area, though we can say with authority that (as you've noticed) that Theravada Buddhism is the most common variety found in them. With Theravada even having state sanctioned support in Thailand, Burma, and Cambodia.

Theravada Buddhism is not my specialty, so allow me to work backwards.

The Buddhism of Tibet, while in practice respectful of Buddhists from southeast Asia, going so far as to be friendly and build relationships with them, especially Thais and Sri Lankans, is in theory hostile to the philosophies inherent in Theravada Buddhism. Theravada Buddhism is a "politically correct" term, "Theravada" meaning something like "the original way of the elders," which is preferable over Hinayana Buddhism, which literally means "The Lesser Vehicle," as opposed to Mahayana Buddhism, "The Greater Vehicle." In Tibetan theg pa chen po (lit. "way" "great") is taken to both mean "big" and "great" as in wonderful. Theg pa dman pa here, the dman pa really does have the connotation of inferior.

Mahayanists hold up the Bodhisattva as the ideal spiritual being (subsidiary only to the Buddha). The Bodhisattva is an enlightened being who refuses Nirvana for the sake of suffering for all sentient beings. Theravadins hold up the Arhat, who is a fully enlightened being who seeks to attain realization and escape the cycle of suffering. Theravadins hold close the Buddha's declaration "tend to your own salvation" (supposedly his dying words) whereas Mahayanists, in general, find this to be egotistical and selfish.

The Nalanda Pandits, in particular, have harsh words for the Theravadins. And it is the Nalanda tradition where we start to see the real formation of Mahayana Buddhism. It is from here that we start to see native Chinese (i.e. Xuanzang of Journey to the West fame, the monk confusingly named I-ching, and others) traveling along the Silk Road and learning Buddhism from the source. While there had been Indian Buddhist teachers traveling to China as well, it was these teachers who learned Buddhism from Mahayanist originators and took their translations of the sutras back to China, developing what we now call the Chinese Canon. Glossing over the complexity of it, we can divide Theravada, Mahayana, and Tibetan (Mahayana and/or Vajrayana depending on the definition) Buddhism casually by their authoritative texts: Theravada Buddhism holds up the Pali Canon, Mahayana Buddhism holds up the Chinese Canon (available and read in Korea, Japan, and yep, Vietnam), while Tibetan Buddhism holds up the Tibetan Canon. The Canons include lots of overlapping texts, but there are gems found in each that are unique. I.e. the famous Milindapanha is found only in Pali, and not in Chinese or Tibetan. The works from the Nalanda tradition will not be found in Pali, but they are legion in the Tibetan.

I'm sure you can see where this is going.

Chinese Buddhism was a loose amorphous blob of religious traditions that eventually formed into schools, lineages, and standardized traditions that received imperial support by the Tang Dynasty. It was from the Tang Dynasty that we see Chan Buddhism emerge in what we might call a mature state, and where it begins spreading from China to Korea, Japan, and Vietnam. While Thailand and Burma received their Sangha traditions mainly from Sri Lankan (i.e. Theravadin) missionaries, Vietnam was (for lack of a better word) colonized by China, and received its cultural foundations and traditions from the north. This includes its Buddhism, descended from the Chinese Mahayana Canon.

To expand upon u/JimeDorje's answer, the south of Vietnam was, at many points, Therevadin, due to heavy influence from Cambodia. For most of Vietnam's history, Vietnam proper only existed in what today is considered the geographical and cultural north. The Dai Viet people only took control of the central and south during the 15th century. Before that, it was occupied by the Cham and the Khmer people respectively. Among these, there was a syncretic Hindu-Mahāyāna sect and Theravada. When Vietnam took over, they drove the Cham to Cambodia and to Malaysia and the Khmer into present day Cambodia due to the brutal campaign. These campaigns were fairly easy due to the recent collapse of the Khmer Empire that had been dominant in the region for the last six centuries.

It should also be noted that the Khmer and the Thai were Mahāyāna, Hindu (primarily Vaiṣṇavist), and Hindu-Buddhist syncretic (primarily Śaivite and Mahāyāna) until fairly recently. The Khmer empire was, until 12th century officially Hindu and after that remained Mahāyāna until the 13th or 14th century. The reasons for this change are unclear and some historians have noted that it lines up with the decline of the Khmer Empire. I would posit that it had to do with the increasing influence of the Mon and Thai people on the Khmer empire. The Thai's had largely converted to Theravāda by the early 13th century with the establishment of Sukhothai with the help of the Mon, who as far as we can tell were the earliest adopters of Buddhism in Southeast Asia and had been Theravāda since at least the 5th century CE, but probably much earlier.

The Theravāda domination of mainland Southeast Asia started with the Mon kingdoms and the Śri Lankān missions in the 5th century as well as the Pyu and Arkan kingdoms in present day Myanmar, who recorded inscriptions in Pāli as early as the 4th century. When the major kingdom of Pagan was established by the Bamar who migrated to the region and converted to Theravāda from a tantric syncretic sect, unifying present day Myanmar, Theravāda was made the state religion. As the Mon expanded and the Bamar state of Pagan became more and more influential, Theravāda became more dominant in the region. By the 15th century Laos, Myanmar, Cambodia, and Thailand were all Theravāda.

However, the division between Mahāyāna and Theravāda wasn't always so clear cut. Mahayāna has never been a distinct sect in the way that it is thought of today. Instead, for most of Buddhism's history the division has been along the lineage of Vinaya, the rules of Buddhism. It is unknown what the Khmer Buddhists followed before the Śrākayāna ("hearer-vehicle" as opposed to the "great vehicle" or "Bodhisattva vehicle") Theravāda, it may have in fact been a Mahāyāna Theravāda, or perhaps the Mahāyāna cult had no true monastic lineage separate from the Theravāda and they existed alongside one another but the Mahayāna was purely devotional cults dedicated to Bodhisattvas and cosmic Buddhas.

Nor does this mean that Mahāyāna went away in the rest of Southeast Asia. Certain Bodhisattva cults and Mahāyāna practices remained, and some still do. San Yank tattoos and Cambodian esoterism likely descend from the Hindu, Mahāyāna, and Vajrayāna practices that predated the orthodox Theravāda.

Sources and Further Reading

• Tai Thu Nguyen, The History of Buddhism in Vietnam. 2008. Vietnamese Academy of Social Sciences, Council for Research in Values and Philosophy.

• Ian Harris. Cambodian Buddhism: History and Practice. 2005. University of Hawai'i Press.

• Michael Aung-Thwin & Maitrii Aung-Thwin. A History of Myanmar Since Ancient Times. 2012. Rektion Books.

• David K. Wyatt. Thailand: A Short History. 2003. Yale University Press.

• Richard F Gombrich. Theravāda Buddhism: A Social History from Ancient Benares to Modern Colombo 2nd Ed. 2006. Routledge Publications.

• Roger Bischoff Buddhism in Myanmar: A Short History. 1995. Wheel Publications.

• Donald K. Swearer. * The Buddhist World of Southeast Asia* 2nd Ed. 2010. SUNY press.