The factions were less differentiated on theological, but rather on ideological, grounds. There also were political and religious groups based on variations of Buddhism, such as the Cao Dai.
Political activities, although a major part of the South Vietnamese governmental power struggles of the 1960s, historically have been outside the traditions of Buddhism in Vietnam. 
Some of the most dramatic events, in Western eyes, were protests by monks, who committed suicide by self-immolation: burning themselves alive. The rationale came from a relatively new Vietnamese tradition not only of personal salvation but of service in social action: "the development of clinics, schools, libraries -- and by extension, political action...[discussed in the book] Engaged Buddhism, by Thich Nhat Hanh, head of the School for Youth for Social Service of the new Van Hanh Buddhist University in Saigon has been present in South Vienam for several decades, it captured widespread attention only in recent years.  The activism centered in Hue, the most Buddhist major city in South Vietnam, and was opposed by many monks and laity in Saigon, the Mekong Delta, and outside Vietnam.
Even though the Vietnamese factions were more politically differentiated, Buddhism itself had its own mainstream Vietnamese version, as well as new sects that were spinoffs from Buddhism, such as the Cao Dai and Hoa Hao.
The core of Vietnamese Buddhism comes from the Mayahana (Greater Way, Ðài Thừa in Vietnamese) rite, but with influences from Confucianism and Taoism.  The Vietnamese tendency to absorb cultural influence and create their own synthesis is essential to understanding the country. Vietnamese cuisine is recognizably Asian, but has French influences, as with a delicately baked cake flavored with a scent-tamed durian custard. In a more serious vein, one cannot understand the governing pattern of Ngo Dinh Diem until one understand his Vietnamese minority Catholic outlook had a strong Confucianist influence.
A major area of conflict was that Ngo Dinh Diem, president from 1954 to his overthrow in 1963 was a Catholic, and gave preferences to the Catholic majority. Even so, there were later events such as the Buddhist crisis of 1966 involving activist Buddhist groups, even though they were protesting against a government whose leaders were primarily Catholic.
In 1966, 11 of 16 Buddhist groups formed a coalition to influence the government. While Tri Quang wanted the political post in the coalition, it went, instead, to Tam Chau, originally from the North, and known for strong anti-Communism rather than Quang's more neutralist orientation. In the 1966 Buddhist crisis, Gen. Nguyen Khanh met with both Quang and Chau. Khanh made a cash payment to the Buddhist alliance, which wanted a veto power over government decisions. In Saigon, the United Buddhist Association has tried without complete success to curb the militants by adopting a code of conduct forbiding political activities by monks.According to a current Socialist Republic of Vietnam website,
in 1981 the Vietnam Buddhist Church was formed with the motto duly inscribed in its Charter: Dharma-Nation-Socialism. Needless to say, radical partisans of the old Unified Buddhist Church violently criticized the newly formed Church as a government sanctioned and controlled puppet organization. At the same time, they claimed that the Unified Buddhist Church of Vietnam was the rightful heir to the 2000-year-old legacy of Vietnamese Buddhism.
Perhaps the most activist major faction was led by Tri Quang. Arguably, he maintained the largest political organization in South Vietnam, other than the Viet Cong. Even Thich Tri Quang and his fellow militants occasionally have insisted they were concerned, only with religion, and not politics.
In March 1966, he allied with corps commander Gen. Nguyen Chanh Thi. Premier Nguyen Cao Ky replaced Thi with Ton That Dinh. When Karnow interviewed Quang, he found him less a politician than seeming to "personify a form of fudamentalism in his passionate effort to preserve Vietnam's venerable values, which both the Americans and the Communists were contaminating...implicitly, too, he was a xenophobe..." The Communists banished him to a monastery in 1975. 
Tam Chau is considered the leader of Buddhists who came to South Vietnam in 1954. He has stated concern over Communist penetration...the monks become involved in politics....but he also Tam Chau has also given his support to Buddhist demands for national elections and the end of military rule but has given clear indications of his willingness to compromise and seek a non-violent solution to the problem. He did call for an end to the 1966 protests.
- Minh Chau, A brief history of Vietnamese Buddhism
- Research & Reference Service, United States Information Agency (June, 1966), Vietnamese Buddhism in Ferment: Part II, the Buddha, the Dharma, and the Sangha, USIS R-110-66, p. i
- USIS R-110-66, p. 6
- , Vietnamese Buddhism, Viet-Nam: Land of Legends and Dragons
- Karnow, Stanley (1983), Vietnam, a History, Viking Press, pp. 339-340
- USIS R-110-66, pp. 12-13
- Minh Chi, An Overview of Vietnamese Buddhism
- Often written Thich Tri Quang; "Thich" is an honorific roughly translated to "venerable"
- "Politician from the Pagoda", Time, April 22, 1966
- USIS R-110-66, p. 12
- Karnow, p. 448-449
- USIS R-110-66, p. 13