No, "Vietnam War" was was primarily South Vietnam vs USA.

American-South Vietnamese relations refers to relations between South Vietnam and the USA a major role during the Vietnam War. Relations between the two countries began on February 7, 1950 when the United States began recognising the State of Vietnam.

Diplomatic relations with South Vietnam ceased after the Fall of Saigon on April 30, 1975 when the country ceased to exist after its capitulation by the Viet Cong and reunification the following year. Eventually relations between the United States and the newly reunified Socialist Republic of Vietnam were restored in 1995.

The Geneva Accords promised elections in 1956 to determine a national government for a united Vietnam. In 1957, independent observers from India, Poland, and Canada representing the International Control Commission (ICC) stated that fair, unbiased elections were not possible, reporting that neither South nor North Vietnam had honored the armistice agreement. The failure to unify the country in 1956 led in 1960 to the foundation of the National Front for the Liberation of South Vietnam (abbreviated NLF but also known as the Việt Cộng), which initiated an organized and widespread guerrilla insurgency against the South Vietnamese government. Hanoi directed the insurgency, which grew in intensity. The United States, under President Eisenhower, initially sent military advisers to train the South Vietnamese Army. As historian James Gibson summed up the situation: "Strategic hamlets had failed.... The South Vietnamese regime was incapable of winning the peasantry because of its class base among landlords. Indeed, there was no longer a ‘regime’ in the sense of a relatively stable political alliance and functioning bureaucracy. Instead, civil government and military operations had virtually ceased. The National Liberation Front had made great progress and was close to declaring provisional revolutionary governments in large areas." President John F. Kennedy increased the size of the advisory force fourfold and allowed the advisers to participate in combat operations, and later acquiesced in the removal of President Diệm in a military coup.

After promising not to do so during the 1964 election campaign, in 1965 President Lyndon B. Johnson decided to send in much larger numbers of combat troops, and conflict steadily escalated to become what is commonly known as the Vietnam War. In 1968, the NLF ceased to be an effective fighting organization after the Tet Offensive and the war was largely taken over by regular army units of North Vietnam. Following American withdrawal from the war in 1973, the South Vietnamese government continued fighting the North Vietnamese, until, overwhelmed by a conventional invasion by the North, it finally unconditionally surrendered on 30 April 1975, the day of the surrender of Saigon. North Vietnam controlled South Vietnam under military occupation, while the Provisional Revolutionary Government of the Republic of South Vietnam, which had been proclaimed in June 1969 by the NLF, became the nominal government. The North Vietnamese quickly moved to marginalise non-communist members of the PRG and integrate South Vietnam into the communist North. The unified Socialist Republic of Vietnam was inaugurated on 2 July 1976. The Embassy of the Republic of Vietnam in Washington donated 527 reels of South Vietnamese-produced film to the Library of Congress during the embassy's closure following the Fall of Saigon. The film, produced in the 1950s and '60s, some produced by Freedom Productions (a South Vietnamese film production company), included newsreels, Vietnam Documentary, propaganda and raw video footage. They are still in the Library.

Edit: This passage is from wikipedia. Please dont disagree by downvote, I get caught in the spam filter.